
244 F.Supp.2d 801 (2003)
Franklin JONES, Petitioner,
v.
Dave SMITH, Respondent.
No. 01-CV-73253-DT.
United States District Court, E.D. Michigan, Southern Division.
January 23, 2003.
*804 Franklin Jones, Detroit, MI, pro se.
Brenda E. Turner, Mich. Dept. of Atty. Gen., Habeas Corpus Div., Lansing, MI, for Dave Smith.

OPINION AND ORDER DENYING PETITION FOR WRIT OF HABEAS CORPUS
ROSEN, District Judge.
Petitioner Franklin Jones ("Petitioner"), a state prisoner currently confined at the Ryan Correctional Facility in Detroit, Michigan, has filed a pro se petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2254 alleging that he is incarcerated in violation of his constitutional rights. Petitioner was convicted of assault with intent to commit great bodily harm less than murder and arson of a dwelling following a jury trial in the Criminal Division of the Wayne County Circuit Court in 1997.[1] He was sentenced to concurrent terms of eleven to twenty years imprisonment *805 for arson and six to ten years for the assault conviction.
In his pleadings, Petitioner asserts claims regarding the admission at trial of statements given to the police without Miranda warnings, exclusion of testimony concerning the reputation and character of the prosecution's investigators and witnesses, and jury instructions. For the reasons stated below, the petition for a writ of habeas corpus will be denied.

I. FACTS
Petitioner's conviction arises from the burning of an occupied two family flat at 16260 Hartwell in Detroit, Michigan, on January 27, 1997. Amaka Jacqueline Onumono, a twenty-two year old African-American woman who lived in the house, suffered severe burns to seventy-five (75) percent of her body as a result of the fire. She was found naked on the floor of the kitchen by Detroit firefighters who responded to the blaze. Blood and mucous were gurgling from her nose and mouth and her breathing was shallow when she was rescued.
According to Dr. Chenicheri Balakrishnan, M.D., a staff surgeon at Detroit Receiving Hospital, Ms. Onumono suffered first degree burns to her face, and second and third degree burns to her lower back and legs. She had suffered a head injury and fractured cheekbone, consistent with being hit or falling. Expert testimony indicated that Ms. Onumono's burns were the result of fire being directly in contact with her body for at least ninety (90) seconds. It was opined that Ms. Onumonu must have been unconscious at the time she was burned, or she would have rolled over and attempted to extinguish the fire. Burns were found on her buttocks, thighs, legs, feet, toes, and right arm. Ms. Onumono also suffered a broken right arm, a fractured neck, and non-displaced fractures of her left cheek bone and C-3 vertebra. Dr. Balakrishnan concluded that Ms. Onumono suffered burns from direct contact of a burning liquid to her skin. To suffer third degree burns as Ms. Onumono did, the burning liquid would have had to have been in contact with her skin for at least ninety seconds with her remaining still so as to not put the fire out.
Petitioner claimed in his last statement to the police and at trial that he and Ms. Onumono had an argument in the kitchen and hot grease from a frying pan spilled causing the fire. Petitioner stated that he tried to put the fire out with a blanket which caught fire. In a prior statement to the police, Petitioner claimed to have been away from the home visiting fast food restaurants when the fire started. In another statement not made to the police, Petitioner stated that the fire may have started when Ms. Onumono tried to manipulate the home's furnace.
No burned blanket was found by fire investigators. Fire Investigator Lt. Albert Hood testified that the fire could not have started the way Petitioner said it did. Lt. Hood further testified that he agreed with other fire department personnel that the fire was caused by a flammable liquid. The fire was caused by the ignition of an accelerant placed at several locations in the house. This contradicted Petitioner's claim that the fire started in one location the kitchen stove area. Lt. Hood concluded that the fire was incendiary in nature and that it originated in the kitchen by the ignition of vapors of a flammable liquid accelerant which was distributed and ignited in the kitchen, dining room, and living room.
Ms. Onumono testified that on the day of the fire Petitioner was angry with her about a new relationship in which she was involved and threatened to kill her. Petitioner and Ms. Onumono had been lovers and had a child together, but had broken *806 up at Ms. Onumono's initiative. At the time of the fire, they no longer had an intimate personal relationship. They remained in contact, however, because they had a daughter together. Nevertheless, Petitioner was wildly jealous of another man Ms. Onumonu was seeing, grilled her about her relationships with other men, and told her, "`I'll kill you bitch."` Trial Transcript ("Tr.") of September 15, 1997 at 189-91. Petitioner and Ms. Onumonu argued in the bedroom. She was dressed at that time. Ms. Onumono remembered losing consciousness and waking up in the hospital severely burned. She did not remember anything else after the argument. Id. at 188-92.
The Michigan Court of Appeals summarized the material facts and evidence follows:
There is no dispute that a dwelling home was damaged by fire. The evidence showed that defendant, Onumono, and her young daughter were the only people in the home. Defendant took the child out to the car, at which time there was no fire and Onumono was lying unconscious on her bed. He went back in, then came out and drove away. When he returned, the house was on fire. The fire investigators testified that the burn pattern left by the fire evinced the use of an accelerant, and the fire could not have started from grease splattered on the stove as defendant had claimed. Onumono's physician testified that she had apparently been burned by some sort of flammable substance in direct contact with her skin. Defendant gave false exculpatory explanations for the fire, which were evidence of guilt.... [2]
The evidence showed that defendant and Onumono had an argument in her bedroom and that defendant threatened to kill her. Their daughter then saw Onumono, who was fully clothed, passed out on the bed. Onumono had a fractured cheek bone, which was consistent with a punch to the face. Onumono was found completely naked on the kitchen floor with severe burns to her body. Her doctor testified that, given the length of time her body was on fire, she must have been unconscious at the time. There was evidence that the fire stalled with the use of accelerant, some of which was apparently poured directly on Onumono's body. As noted above, there was circumstantial evidence that defendant set the fire while he was alone in the house with Onumono. Such evidence was sufficient to enable a rational trier of fact to conclude beyond a reasonable doubt the defendant intended to kill Onumono.
People v. Franklin Jones, Jr., No. 208819, 1999 WL 33429982 at 2 (Mich.Ct.App. Nov.23, 1999).
The jury convicted Petitioner of assault with intent to commit great bodily harm less than murder and arson. The trial court subsequently sentenced him to concurrent prison terms of eleven to twenty years for the arson conviction and a six and a half to ten years for the assault conviction.

II. PROCEDURAL HISTORY
Following sentencing, Petitioner filed an appeal as of right with the Michigan Court *807 of Appeals, which affirmed his convictions and sentences in a per curiam decision. People v. Franklin Jones, Jr., No. 208819C, 1999 WL 33429982 (Mich.Ct.App. Nov.23, 1999)(unpublished). Petitioner then filed an application for leave to appeal with the Michigan Supreme Court, which was denied in a standard order. People v. Franklin Jones, 462 Mich. 870, 616 N.W.2d 688 (May 31, 2000).
Petitioner filed the instant petition for a writ of habeas corpus on or about August 30, 2001, raising the following claims as grounds for relief:
I. The trial court erred by allowing the admission of Mr. Jones's un-Mirandized inculpatory statements.
II. Mr. Jones was denied a fair trial when the trial court excluded testimony to show the reputation and character of the prosecution's investigators/witnesses.
III. The lack of sufficient jury instructions both curative and on specific intent compromised the jury verdict and denied Mr. Jones a fair trial.
Respondent filed an answer to the petition on or about January 30, 2002, contending that it should be denied because the claims are unexhausted as federal constitutional claims and/or lack merit, or are not cognizable on habeas review.

III. STANDARD OF REVIEW
The provisions of the Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA"), codified at 28 U.S.C. § 2241 et seq., govern this case because Petitioner filed this habeas petition after the AEDPA's effective date. See Lindh v. Murphy, 521 U.S. 320, 336, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997). The AEDPA provides:
An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or
(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d)(1996).
In Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), the United States Supreme Court undertook a detailed analysis of the correct standard of review under the AEDPA. According to the Supreme Court:
Under § 2254(d)(1), the writ may issue only if one of the following two conditions is satisfiedthe state-court adjudication resulted in a decision that (1) "was contrary to ... clearly established Federal law, as determined by the Supreme Court of the United States," or (2) "involved an unreasonable application of ... clearly established Federal law, as determined by the Supreme Court of the United States." Under the "contrary to" clause, a federal habeas court may grant the writ if the state court arrives at a conclusion opposite to that reached by this Court on a question of law or if the state court decides a case differently than this Court has on a set of materially indistinguishable facts. Under the "unreasonable application" clause, a federal habeas court may grant the writ if the state court identifies the correct governing principle from this Court's decisions but unreasonably applies that principle to the facts of the prisoner's case. *808 Id. at 412-13, 120 S.Ct. 1495 (O'Connor, J., delivering the opinion of the Court on this issue).
In evaluating a state court decision under the "unreasonable application" clause, the Supreme Court further stated that a federal habeas court "should ask whether the state court's application of clearly established federal law was objectively unreasonable." Id. at 411. "Under § 2254(d)(1)'s `unreasonable application' clause, then, a federal habeas court may not issue the writ simply because the court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly. Rather, that application must also be unreasonable." Id.
The Supreme Court also clarified that the phrase "clearly established Federal law, as determined by the Supreme Court of the United States," refers to "the holdings, as opposed to the dicta, of [the Supreme Court's] decisions as of the time of the relevant state-court decision." Id. at 412. In determining what constitutes clearly established federal law, therefore, a federal habeas court must look to pertinent United States Supreme Court precedent.
Lastly, § 2254(e)(1) requires that this Court presume the correctness of state court factual determinations. 28 U.S.C. § 2254(e)(1). A habeas petitioner may rebut this presumption only with clear and convincing evidence. Warren v. Smith, 161 F.3d 358, 360-61 (6th Cir.1998).

IV. DISCUSSION

A. Miranda Violation Claim
Petitioner first asserts that he is entitled to habeas relief because the trial court admitted a false inculpatory statement he made to the police prior to being given Miranda warnings. Respondent contends that the Michigan courts' determinations that the challenged statements were admissible because Petitioner made them spontaneously and not in response to interrogation or its functional equivalent are correct and reasonable determinations of federal constitutional law.
The Michigan Court of Appeals rejected this claim with the following analysis:
Defendant was in custody when he made the statement at issue. Based on the whole record, we agree with the trial court's finding that defendant's statement was made spontaneously and not in response to questioning or its functional equivalent. Therefore, the statement was admissible despite the absence of Miranda warnings.
People v. Franklin Jones, Jr., 1999 WL 33429982 at *2.
Petitioner made the challenged statement while riding in the back seat of a police car from Grace Hospital where he was arrested to the police station. It is undisputed that Petitioner was in custody and had not received Miranda warnings at that time. It is also undisputed that the only question asked of Petitioner prior to his making the challenged statement in the police car was whether both children in the hospital were his. Petitioner replied in the negative to this question.[3] Petitioner *809 claims that, while no further explicit questioning occurred in the police car, his statement was nonetheless the product of the functional equivalent of interrogation.
Officer Vicki Yost testified as follows regarding the circumstances surrounding the statement Petitioner made in the police car and the content of the statement:
Q: Okay. Tell the jury what, what the circumstances, what was going on, how did this lead up to Mr. Jones saying whatever he said?
A: Mr. Jones was very upset. He was handcuffed behind his back. He was rocking back and forth in the seat stating that she's got to be okay. Repeating that. And he just went out to get some food. I only gone out [sic] a couple of minutes and he continued to ramble with similar statements.
Q: That he was gone for a few minutes to get some food?
A: Right. He said where he went. It's in my PCR to [sic], I don't remember the specific restaurant that he said.
Q: If that refreshes your memory, you can check that out?
A: He said that he had gone to Wendy's and Burger King and all the lines were two [sic] long, that's the extent of it.
Q: Okay. Did he say anything else?
A: Yes. That he couldn't get in, he told the neighbor to call
Q: Okay. Now other than, okay. Other than making these statements, do you question Mr. Jones on the way, do you ask him any questions?
A: No sir.
Tr. September 16, 1997 at 124-125.[4]
Law enforcement officers must give "Miranda warnings" before interrogating individuals in custody. See Miranda v. Arizona, 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694 (1966). In Miranda, the Supreme Court held that an individual in police custody may not be interrogated until and unless he is first advised that he has the right to remain silent; that anything he says may be used against him; that he has the right to an attorney; and that an attorney will be appointed for him if he cannot retain one. These warnings are an "absolute prerequisite to interrogation," said the court, 384 U.S. at 467, 86 S.Ct. at 1624, and without the warnings, the fruits of a custodial interrogation are inadmissible at trial. The Supreme Court held that: "To summarize, we hold that when an individual is taken into custody or otherwise deprived of his freedom by the authorities in any significant way and is subjected to questioning, the privilege against self-incrimination is jeopardized. Procedural safeguards must be employed to protect the privilege.... But unless and until such warnings are demonstrated ..., no evidence obtained as a result of interrogation can be used against him." Miranda v. Arizona, 384 U.S. at 478-479, 86 S.Ct. at 1630 (footnote omitted). Miranda, then, creates procedural safeguards to secure the Fifth Amendment privilege against self-incrimination while a person is subject to custodial interrogation.
The trial court and the Michigan Court of Appeals found that Petitioner's *810 statement made in the police car was admissible because it was a voluntary statement which was not made in response to custodial interrogation. The special procedural safeguards outlined in Miranda are required not merely when a suspect is taken into custody, but instead where a suspect in custody is subjected to interrogation. Rhode Island v. Innis, 446 U.S. 291, 300, 100 S.Ct. 1682, 64 L.Ed.2d 297 (1980)." `Interrogation', as conceptualized in the Miranda opinion, must reflect a measure of compulsion above and beyond that inherent in custody itself." Id. Miranda warnings are required whenever a person in custody is subject either to express questioning or its "functional equivalent". Rhode Island v. Innis, 446 U.S. at 300-301, 10) S.Ct. 1682, 64 L.Ed.2d 297; United States v. Koubriti 199 F.Supp2d 656, 666-67 (E.D.Mich.2002).
A custodial interrogation is defined as " `questioning initiated by law enforcement officers after a person has been taken into custody or otherwise deprived of his freedom of action in any significant way.'" Oregon v. Mathiason, 429 U.S. 492, 494, 97 S.Ct. 711, 50 L.Ed.2d 714 (1977)(quoting Miranda, 384 U.S. at 444, 86 S.Ct. 1602). This includes both express questioning and its "functional equivalent..., actions on the part of police ... that the police should know are reasonably likely to elicit an incriminating response from the subject." Rhode Island v. Innis, 446 U.S. at 301, 100 S.Ct. 1682; United States v. Clark, 982 F.2d 965, 968 (6th Cir.1993).
In the seminal Sixth Amendment case of Brewer v. Williams, 430 U.S. 387, 97 S.Ct. 1232, 51 L.Ed.2d 424 (1977), without discussing the Miranda issue raised, the Supreme Court addressed the sole issue of whether, under the facts present, respondent Williams had been deprived of his Sixth Amendment right to the assistance of counsel. The essential factual background was that Williams was convicted of the murder of a ten year old girl and his conviction was affirmed by the Iowa Supreme Court. A federal district court granted Williams habeas relief on the grounds that statements he made to police officers while being moved by automobile 160 miles were not voluntary. A divided Court of Appeals for the Eighth Circuit affirmed.
Before surrendering himself to the Davenport, Iowa police, Williams had contacted his lawyer, Henry McKnight, in Des Moines, who advised Williams to surrender. McKnight then went to the Des Moines police station and told the Des Moines police that he had talked to Williams and instructed him to surrender to the Davenport police. When the Davenport police called the Des Moines police to tell them that Williams had surrendered, McKnight again conversed with his client:
"In the presence of the Des Moines Chief of Police and a Police Detective named Learning, McKnight advised Williams that Des Moines police officers would be driving to Davenport to pick him up, that the officers would not interrogate him or mistreat him, and that Williams was not to talk to the officers about Pamela Powers (the murdered girl) until after consulting with McKnight upon his return to Des Moines. As a result of these conversations, it was agreed between McKnight and the Des Moines police officials that Detective Learning and a fellow officer would drive to Davenport to pick up Williams, that they would bring him directly back to Des Moines, and that they would not question him during the trip."
Id. at 391, 97 S.Ct. at 1235, 51 L.Ed.2d at 431-432.
Before they left for Des Moines, Williams met with a Davenport attorney named Kelly who "reiterated to Detective *811 Learning that Williams was not to be questioned about the disappearance of Pamela Powers until after he had consulted with McKnight back in Des Moines". Id. at 391, 97 S.Ct. at 1236, 51 L.Ed.2d at 432.
However, during the trip to Des Moines, Detective Learning gave what later became known as the "Christian burial speech," in which he spoke of the snowy weather conditions, the difficulty of finding the slain girl's body in such weather, the fact that the ten year old girl had been taken from her parents on Christmas Eve, and that her parents were entitled to provide a Christian burial for their little girl. After hearing this speech by Learning, Williams revealed the location of the girl's body.
The Supreme Court found that Learning's Christian burial speech was a form of interrogation:
There can be no (serious) doubt, ... that Detective Learning deliberately and designedly set out to elicit information from Williams just as surely as and perhaps more effectively than if he had formally interrogated him. Detective Learning was fully aware before departing for Des Moines that Williams was being represented in Davenport by Kelly and in Des Moines by McKnight. Yet he purposely sought during Williams' isolation from his lawyers to obtain as much incriminating information as possible.
Id. at 399, 97 S.Ct. at 1239-1240, 51 L.Ed.2d at 436-437.[5]
Nothing said by the police while Petitioner was being transported from Grace Hospital to police headquarters was in any way comparable to the "Christian burial" speech of Brewer v. Williams, supra. No statements were made, such as, for example, that only a monster could have done this to Ms. Onumono, prompting Petitioner to try to exculpate himself. It has not been alleged that the police threatened Petitioner in any way during the ride to the police station. Petitioner has not alleged that the police threatened him or coerced him in the police car. Thus, there is no evidence or allegation that Petitioner was subjected to any functional equivalent of interrogationwhether in the form of a subtle emotional appeal, or in the form of harsh threat or coercionduring his ride to the police station.
Simply riding to the police station in a police car accompanied by uniformed officers while being under arrest is not the "functional equivalent of interrogation." If it were, Miranda`s prohibition against unwarned statements made in response to custodial interrogation would be transformed into a blanket prohibition against admission of any unwarned statements made in custody. In fact, Miranda simply does not prohibit admission of statements made in custody unless they are the product of questioning (interrogation) or its functional equivalent. Rhode Island v. Innis, 446 U.S. at 300-301, 100 S.Ct. 1682; United States v. Koubriti, 199 F.Supp2d 656, 666-67 (E.D.Mich.2002).
In the present case, the Michigan Court of Appeals determined that Petitioner's statement made in the police car was voluntary and was not made in response to any interrogation. A state court's finding that no express interrogation of a habeas petitioner occurred is a factual finding which is entitled to the presumption of correctness. Dell v. Straub, 194 F.Supp.2d 629, 646 (E.D.Mich.2002). Petitioner has offered no evidence to rebut the *812 trial court's Michigan Court of Appeals' finding that Petitioner's first statement was not the result of custodial interrogation, but was voluntarily made. This Court must accept this finding as true for habeas purposes.
Further, the record shows that Petitioner acknowledged that the only question he was asked while in the police car was whether both children at the hospital were his. This question was not reasonably likely to elicit an incriminating response from Petitioner and did not constitute the functional equivalent of interrogation regarding the fire or Ms. Onumono's beating. Nor was Petitioner subjected to any threats, intimidation, or coercion which might be deemed a functional equivalent of interrogation.
Where a defendant makes a voluntary statement without being questioned or pressured by the police, the statements are admissible despite the absence of Miranda warnings. United States v. Murphy, 107 F.3d 1199, 1204 (6th Cir.1997) (internal citations omitted); United States v. Koubriti, 199 F.Supp.2d at 666-67. "[I]t is well settled that a volunteered statement made by a suspect, not in response to interrogation, is not barred by the Fifth Amendment and is admissible with or without the giving of Miranda warnings." United States v. Thornton, 17 F.Supp.2d 686, 693 (E.D.Mich.1998) (Gadola, J.). The record shows that Petitioner made his statement in the police car without being questioned or pressured by the police.
This Court concludes that the decisions of the trial court and Michigan Court of Appeals that Petitioner's statement made in the police car was admissible because it was voluntarily offered and not made in response to custodial interrogation or threats are reasonable applications of controlling federal constitutional law. Therefore, Petitioner's Miranda claim does not entitle him to habeas relief.
However, even if the trial court erred permitting the testimony concerning Petitioner's statement made in the police car, Petitioner has failed to show that such error had a substantial and injurious effect on the jury's verdict of conviction.
Prior to 1993, the test for harmless error for federal courts on habeas review of state court determinations was set forth in Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). Under the Chapman standard, "[a]n error is harmless only when the court, after assessing `the record as a whole to determine the probable impact of the improper evidence on the jury,' can conclude beyond a reasonable doubt that the error did not influence the jury's verdict." Williams v. Zahradnick, 632 F.2d 353, 360-61 (4th Cir.1980). The Chapman test, therefore, is not whether laying aside the erroneously admitted evidence there was other evidence sufficient to convict beyond a reasonable doubt (a test that undoubtedly would be met here), but, more stringently, "whether there is a reasonable possibility that the evidence complained of might have contributed to the conviction." Fahy v. Connecticut, 375 U.S. 85, 86-87, 84 S.Ct. 229, 230-231, 11 L.Ed.2d 171 (1963); see generally R. Traynor, The Riddle of Harmless Error 43-44 (emphasizing strictness of the Chapman test).
However, in 1993, however, the Supreme Court in Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993), specifically held that Chapman no longer applied to federal habeas review of state court harmless error decisions, although state courts would still be required to apply that standard on direct review. Instead, the Supreme Court adopted a new test that requires federal courts on habeas review of constitutional *813 trial errors to determine whether the error "had substantial and injurious effect or influence in determining the jury's verdict." Brecht, 507 U.S. at 637, 113 S.Ct. at 1722 (citation omitted). Consequently, federal courts are to use and follow Brecht when reviewing habeas petitions of constitutional trial errors based on state court determinations of harmless error. Furthermore, the harmless error standard announced in Brecht applies even if a federal habeas court is the first to review for harmless error. Gilliam v. Mitchell, 179 F.3d 990, 995 (6th Cir.1999); see also O'Neal v. McAninch, 513 U.S. 432, 445, 115 S.Ct. 992, 130 L.Ed.2d 947 (1995) (habeas court should grant petition if it has "grave doubt" about whether trial error had substantial and injurious effect or influence upon the jury's verdict). Thus, habeas relief may only be granted where trial error has a "substantial and injurious effect" on the jury's verdict.
Petitioner has not made this showing. Petitioner was not directly impeached with his statement made in the police car. Tr. September 18, 1997, at 74-90. Furthermore, Petitioner's version of how the fire started was effectively refuted by the testimony of Amaka Onumono, Petitioner and Ms. Onumono's daughter, Desera Jones; Dr. Balakrishnan, and the Fire Department investigators. Petitioner's false exculpatory statements made at trial also provided powerful evidence of his guilt. The testimony of Officer Yost regarding Petitioner's statement made in the police car had slight weight.
Thus, Petitioner has not shown that any error in admitting Officer Yost's testimony about Petitioner's statement made in the police car had a substantial and injurious effect on the jury's verdict. Therefore, for all of the above-stated reasons, Petitioner's Miranda claim lacks merit.

B. Evidentiary Claim
Petitioner contends that he was denied due process when the trial court excluded testimony intended to show the character of an investigating officer. Petitioner sought to cross-examine police homicide investigators regarding allegations of investigative improprieties in other homicide investigations.[6] The trial court refused to admit this evidence finding that it was not calculated to test the witnesses' credibility in this case and, therefore, was irrelevant and inadmissible. M.R.E. 401, 402. Further, defense counsel abandoned this line of inquiry regarding one investigator in response to the prosecutor's objection. Therefore, Petitioner waived that claim of alleged error.
One well established rule, not altered by the AEDPA, is that "[a] federal court may not issue the writ on the basis of a perceived error of state law." Pulley v. Harris, 465 U.S. 37, 41, 104 S.Ct. 871, 875, 79 L.Ed.2d 29 (1984); see Floyd v. Alexander, 148 F.3d 615, 619 (6th Cir.) (concluding that violation of a state law is not cognizable in federal habeas corpus proceedings), cert. denied, 525 U.S. 1025, 119 S.Ct. 557, 142 L.Ed.2d 464 (1998); Moore v. Tate, 882 F.2d 1107, 1109 (6th Cir.1989) ("It is well established that `[w]hile habeas review does not ordinarily extend to state court rulings on the admissibility of evidence ... [however] an erroneous evidentiary ruling which renders a trial fundamentally unfair warrants a writ of habeas corpus.' ") (citing Fuson v. Jago, 773 F.2d 55, 59 (6th Cir.1985)).
Accordingly, Petitioner's state law claim concerning exclusion of alleged evidence of *814 improprieties by homicide investigators in other, unrelated cases is not cognizable on habeas review. See Floyd, 148 F.3d at 619; see also 28 U.S.C. § 2254(a).
Even if Petitioner had raised this claim as a federal constitutional issue, he would have to show that the alleged evidentiary error so perniciously affected the prosecution of his case that it deprived him of the fundamental right to a fair trial to be entitled to habeas relief.
Errors in rulings regarding the admission or exclusion of evidence, are usually not grounds for federal habeas relief. Cooper v. Sowders, 837 F.2d 284, 286 (6th Cir.1988). Violations of state law and procedure which do not infringe specific federal constitutional rights are generally not cognizable in habeas corpus. "An evidentiary ruling is a cognizable ground for federal habeas corpus relief if it deprived the state court defendant of fundamental fairness." Bundy v. Dugger, 850 F.2d 1402, 1422 (11th Cir.1988). However, the reviewing court will only grant federal habeas corpus relief where a violation of a state's evidentiary rule results in the denial of fundamental fairness, and therefore, a violation of due process. Id. As the Eleventh Circuit stated, the standard in determining whether an erroneous evidentiary ruling "constitutes a denial of fundamental fairness is whether the evidence is material in the sense of a crucial, critical, highly significant factor." Leverett v. Spears, 877 F.2d 921, 925 (11th Cir.1989)(internal citations omitted).
A criminal defendant's right to confront the prosecution's witnesses for the purpose of challenging their testimony and right to present his own witnesses to establish a defense are fundamental components of due process of law. Washington v. Texas, 388 U.S. 14, 19, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967); See also, Chambers v. Mississippi 410 U.S. 284, 294, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973)(the rights to confront and cross-examine witnesses and to call witnesses on one's own behalf have long been recognized as essential to due process). Criminal defendants have a Fifth and Sixth Amendment right to present witnesses that are both material and favorable. Taylor v. Singletary, 122 F.3d 1390, 1394 (11th Cir.1997)(citing United States v. Valenzuela-Bernal 458 U.S. 858, 102 S.Ct. 3440, 73 L.Ed.2d 1193)((1982)). Further, the Sixth Amendment Confrontation Clause guarantees the defendant the right to cross examine adverse witnesses to uncover possible biases and expose the witness's motivation in testifying. See Davis v. Alaska, 415 U.S. 308, 315-16, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). Unduly restricting a defendant's ability to cross-examine a prosecution witness may violate his Sixth Amendment right of confrontation. Id. at 316, 94 S.Ct. 1105.
However, a federal habeas court will not disturb a state court's exclusion of evidence which it finds is irrelevant unless the relevance and probative value of such evidence is so apparent and great that excluding the evidence denies the petitioner the due process of law. Hopkinson v. Shillinger, 866 F.2d 1185, 1197 (10th Cir.1989); Cosme v. Elo, 2000 WL 246592, * 3 (E.D.Mich. February 4, 2000) (Cohn, J). The inquiry in reviewing a claim of improper exclusion of evidence is whether the evidence was rationally connected to the crime charged and, if its exclusion was so prejudicial as to deprive the defendant of a fundamentally fair trial. Carter v. Jago, 637 F.2d 449, 457 (6th Cir.1980).
In the present case, the testimony sought to be admitted concerning alleged improprieties in other homicide cases was not material, critical, or even relevant to Petitioner's case. Furthermore, the key evidence against Petitioner was not offered by homicide investigators, but by Amaka
*815 Onumono, Petitioner and Ms. Onumono's daughter Desera Jones, Dr. Balakrishnan, and the Fire Department investigators. Petitioner has not shown that exclusion of the proffered evidence was improper or deprived him of a fair trial. Therefore, this claim does not entitle him to habeas relief.

C. Jury Instructions Claim
Petitioner contends that he was denied a fair trial by the lack of a curative instruction and improper instructions on the specific intent required to find him guilty of the crimes charged. These jury instruction claims lack merit.
Petitioner contends that he was denied a fair trial by the absence of a curative instruction regarding an unredacted written statement. The dispute involved questions of what material Petitioner had wanted included in a statement he gave to Lieutenant Hood and what material he did not. Petitioner waived this issue in state court by failing to request the instruction there. The Michigan Court of Appeals enforced this default and found that "[inasmuch as the matter did not pertain to a basic and controlling issue in the case, manifest injustice will not result from our failure to review the issue." Jones, 1999 WL 33429982 at *3. Consequently, this claim is procedurally defaulted.
Petitioner's habeas claim is barred by the doctrine of procedural default because Petitioner failed to appeal the challenged jury instruction omission to the state courts as provided by Michigan law. A state prisoner's habeas corpus claims are procedurally defaulted if the prisoner has failed to comply with an independent and adequate state procedural rule, thus causing default of the prisoner's federal claims in state court. Coleman v. Thompson, 501 U.S. 722, 750, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). This can occur when an individual fails to present an issue to a state appellate court upon the only opportunity to do so. Teague v. Lane, 489 U.S. 288, 297-98, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989); Rust v. Zent, 17 F.3d 155, 160 (6th Cir.1994).
Petitioner did not seek the curative instruction regarding his unredacted statement in the trial court. Hence, he procedurally defaulted this claim. When a petitioner has procedurally defaulted a claim in the state courts, the claim may be raised on habeas review only if the petitioner can demonstrate "cause" and "actual prejudice," see Murray v. Carrier, 477 U.S. 478, 485, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986), or show that a fundamental miscarriage of justice has occurred. Id. at 496, 106 S.Ct. 2639. To establish cause, a petitioner must establish that some external impediment frustrated his ability to comply with the state's procedural rule. See Murray, All U.S. at 488, 106 S.Ct. 2639. A petitioner must present a substantial reason to excuse the default. See Amadeo v. Zant, 486 U.S. 214, 223, 108 S.Ct. 1771, 100 L.Ed.2d 249 (1988); Rust, 17 F.3d at 161. Petitioner neither alleges nor establishes sufficient cause to excuse his failure to seek this instruction in the trial court.
Nor has Petitioner introduced any reliable new evidence of his innocence. Hence, Petitioner has not established that a fundamental miscarriage of justice has occurred. The miscarriage of justice exception requires a showing that a constitutional violation probably resulted in the conviction of one who is actually innocent. Schlup v. Delo, 513 U.S. 298, 326-27, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995)." `[Actual innocence' means factual innocence, not mere legal insufficiency." Bousley v. United States, 523 U.S. 614, 624, 118 S.Ct. 1604, 140 L.Ed.2d 828 (1998). "To be credible, [a claim of actual innocence] requires petitioner to support his allegations *816 of constitutional error with new reliable evidencewhether it be exculpatory scientific evidence, trustworthy eyewitness accounts, or critical physical evidencethat was not presented at trial." Schlup, 513 U.S. at 324, 115 S.Ct. 851. Petitioner has made no such showing. This jury instruction claim is thus barred by procedural default, lacks merit, and does not warrant habeas relief.
Petitioner also contends that the trial court improperly instructed the jury regarding specific intent. In order for habeas corpus to be warranted on the basis of incorrect jury instructions, a petitioner must show more than the instructions are undesirable, erroneous or universally condemned; taken as a whole, they must be so infirm that they rendered the entire trial fundamentally unfair. See Estelle v. McGuire, 502 U.S. 62, 72, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991); Henderson v. Kibbe, 431 U.S. 145, 154, 97 S.Ct. 1730, 52 L.Ed.2d 203 (1977); Scott v. Mitchell, 209 F.3d 854, 882 (6th Cir.2000); cert. den. 531 U.S. 1021, 121 S.Ct. 588, 148 L.Ed.2d 503 (2000). Allegations of trial error raised in challenges to jury instructions are reviewed for harmless error by determining whether they had a substantial and injurious effect or influence on the verdict. Id. Furthermore, In conducting habeas review, the question is "whether the ailing instruction by itself so infected the entire trial that the resulting conviction violates due process." Estelle v. McGuire, 502 U.S. at 72, 112 S.Ct. 475 (quoting Cupp v. Naughten, 414 U.S. 141, 147, 94 S.Ct. 396, 38 L.Ed.2d 368 (1973)).
Review of the record shows that the trial judge properly instructed the jury regarding the specific intent required to prove the crimes of assault with intent to murder, which he stated required that the prosecution prove that Petitioner intended to murder Amaka Onumono; assault with intent to commit great bodily harm less than murder, which he stated required the prosecutor to prove that Petitioner intended to do great bodily harm less than murder to Amaka Onumono; and arson, which he stated required the prosecutor to prove that Petitioner intentionally set a fire which damaged property or a person knowing that this would cause injury or damage to another person or to property and that the he did so without just cause or excuse. See, People v. Taylor, 422 Mich. 554, 375 N.W.2d 1 (1985)(actual intent to kill is required for assault with intent to murder); People v. Compian, 38 Mich.App. 289, 196 N.W.2d 353 (1972)(great bodily harm may be defined as "serious injury of an aggravated nature"); People v. Losinger, 331 Mich. 490, 50 N.W.2d 137 (1951), cert. denied, 343 U.S. 911, 72 S.Ct. 644, 96 L.Ed. 1327 (1952)(intentionally set fire which causes slight damage to building or property is sufficient to prove arson, destruction of building or property need not be proved). Tr. Sept. 18, 1997, at 161-162, 166-167, 171-172.
The trial judge also instructed the jury that Petitioner's intent could be proved by what he said, what he did, how he did it, or by any other facts and circumstances in evidence. Tr. Sept. 18, 1997, at 172.
Petitioner beat and burned the victim on January 26, 1997. The victim suffered a fractured cheekbone, a broken right arm, a fracture of the C-3 vertebra, a concussion, and memory loss from the beating Petitioner inflicted upon her. The victim also suffered smoke inhalation, first and second degree burns on much of her body, and third degree burns on her lower back, arms, legs, and feet. Some of her toes were burned off. At the time of trial, on September 16, 1997, about nine months after the fire, she had not regained full use of her legs and right arm and was still in a wheelchair. Tr. Sept. 15, 1997 at 110-138; Tr. Sept. 16, 1997, at 5-6. Given the horrific *817 nature and extent of the victim's injuries, this Court concludes that Petitioner was not prejudiced by the trial court limiting its definition of great bodily harm to "physical injury that seriously permanently harms the health or function of the body." Tr. Sept. 18, 1997, at 162.
This Court concludes that the trial judge's instructions, taken as a whole, adequately instructed the jury about the intent elements and the other elements required to find Petitioner guilty of the crimes charged. The instructions were not incorrect, much less so infirm that they rendered the entire trial fundamentally unfair. Consequently, this claim lacks merit and does not warrant habeas relief.

V. CONCLUSION
For the reasons stated, this court concludes that Petitioner is not entitled to federal habeas relief on the claims presented. Accordingly,
IT IS ORDERED that the petition for a writ of habeas corpus is DENIED WITH PREJUDICE.
NOTES
[1]  Petitioner was charged with assault with intent to commit murder, but was acquitted of this charge.
[2]  Petitioner gave one false exculpatory statement regarding the cause and nature of the fire referred to in this passage of the Michigan Court of Appeals opinion in response to custodial interrogation by Homicide Investigator Barbara Simon at the police station after receiving Miranda warnings. See Tr. September 16, 1997, at 129-145. Petitioner's Miranda claim is not based on the admission of this warned statement. Rather, his Miranda claim is based on a statement he made in a police car after his arrest before receiving Miranda warnings.
[3]  At a motion hearing Petitioner testified as follows regarding whether he was questioned after his arrest while being transported to police headquarters:

Q: What question was that she [Officer Vicki Yost] asked you?
A: She asked me was both the children in the hospital mine.
Q: You said yes?
A: No sir, I said no.
Q: Okay. And that was the only question that she asked you?
A. Yes, sir.
Q: None of the other officers in that car asked any questions, right?
A: No sir.
Motion Transcript, July 16, 1997, at 101
[4]  In the police car Petitioner stated that he left the house and went to two restaurants and when he returned he saw the fire and told the neighbors to call the fire department. The jury was informed of this statement. However, at trial, Petitioner testified that he was in the home when the fire started accidentally from overheated grease in a skillet in the kitchen. However, the prosecutor did not directly impeach Petitioner on cross-examination with his pretrial statement made in the police car that he had not been in the home when the fire started. Tr. September 18, 1997, at 74-90.
[5]  The Supreme Court in Innis stated that interrogation in the Fifth and Sixth Amendment contexts is not "necessarily interchangeable," 446 U.S. at 300, 100 S.Ct. at 1689, n. 4. However, the Supreme Court did not foreclose the possibility that in looking at this problem, decisions in one context might not inform decisions in the other context.
[6]  Although the victim Amaka Onumono did not die as a result of her injuries, her condition was critical and it was initially thought that she might not survive her injuries. Additionally, Petitioner was initially charged with assault with intent to murder Consequently, the police investigation of the case was handled by the homicide division.
