
962 A.2d 772 (2009)
290 Conn. 209
STATE of Connecticut
v.
Pedro CARRASQUILLO.
No. 17568.
Supreme Court of Connecticut.
Argued March 13, 2008.
Decided January 27, 2009.
*773 Suzanne Z. Curtis, assistant public defender, for the appellant (defendant).
Timothy J. Sugrue, senior assistant state's attorney, with whom, on the brief, was Michael Dearington, state's attorney, for the appellee (state).
ROGERS, C.J., and PALMER, VERTEFEUILLE, ZARELLA and SCHALLER, Js.
PALMER, J.
The defendant, Pedro Carrasquillo, was arrested and charged with, inter alia, murder in violation of General Statutes § 53a-54a.[1] Because the defendant was fifteen years old at the time of the offense, his case automatically was transferred from the juvenile docket to the regular criminal docket in accordance with General Statutes (Rev. to 2003) § 46b-127 (a).[2] A jury found the defendant guilty of murder,[3] and the trial court thereafter sentenced the defendant to a term of thirty-five years imprisonment pursuant to General Statutes § 53a-35a(2),[4] which requires a mandatory minimum prison term of twenty-five years for the crime of murder.[5] On appeal,[6] the defendant claims that (1) because he was only fifteen years old when he committed the murder, the statutory scheme subjecting him to a twenty-five year mandatory minimum sentence violates the cruel and unusual punishments clause of the eighth amendment to the United States constitution,[7] and (2) his *774 right to a fair trial was violated when the state's attorney, during closing argument, improperly attributed a motive to the defendant that was unsupported by the evidence. We reject both claims and, accordingly, affirm the judgment of the trial court.
The jury reasonably could have found the following facts. In the early evening of June 16, 2003, the victim, seventeen year old Chauncey Robinson, drove his car to the Moon Mart convenience store on Whalley Avenue in New Haven to purchase cigarettes and candy. Samuel Redd, who was shopping in a nearby shoe store, saw the victim get out of his car and go into the convenience store. Although Redd did not know the victim personally, it was his understanding that the victim had fired a gun in Redd's neighborhood, which angered Redd. When the victim exited the convenience store, Redd, who was wearing a red shirt, followed him to his car with the intent of starting a fight. The victim, however, was able to enter his car before Redd could catch up to him. When Redd reached the victim's car, he kicked in the driver's side window and then fled. As Redd started to run away, he noticed the defendant, with whom Redd was on friendly terms, walking across Whalley Avenue in the direction of the victim's car. A few moments later, Redd heard gunshots.
At the same time that Redd was running from the victim's car, thirteen year old L.C.[8] was coming out of a restaurant located across the street from the victim's parked car. He observed the defendant, whom he knew by name because they attended the same middle school, cross Whalley Avenue and head toward the victim's car. Shortly thereafter, L.C. heard gunshots and started running toward his home. As he was running, he looked back and saw the defendant fire several shots into the front driver's side window of the victim's car. When L.C. arrived home, he told his mother what he had seen, and she immediately telephoned the police. Ismail Nasser, the owner of the Moon Mart convenience store where the victim had purchased cigarettes and candy, also heard the gunshots and ran outside. When he arrived, he observed two people running away. One of them was wearing a red shirt and the other was carrying a gun in his hand. He also observed the victim, who had been shot, slouched in the front seat of his car.
The following procedural history also is relevant to our resolution of the defendant's claims. The defendant was arrested on July 2, 2003, and charged with the victim's murder. Because the defendant was fifteen years old at the time of the offense, his case was transferred from the juvenile docket to the regular criminal docket in the judicial district of New Haven in accordance with § 46b-127 (a), which provides that a child of fourteen or fifteen years of age who has been charged with a class A felony shall be tried and sentenced as an adult. The defendant elected a jury trial.
Prior to trial, the defendant filed a motion to dismiss or, in the alternative, a transfer of his case back to the juvenile docket for treatment as a delinquency matter. The defendant claimed that his automatic transfer to the regular criminal docket pursuant to § 46b-127 (a), and his exposure to the same twenty-five year mandatory minimum sentence applicable *775 to persons sixteen years or older under § 53a-35a(2), constituted cruel and unusual punishment in violation of the eighth amendment to the United States constitution. In support of his claim, the defendant relied primarily on Roper v. Simmons, 543 U.S. 551, 568, 578, 125 S.Ct. 1183, 161 L.Ed.2d 1 (2005), in which the United States Supreme Court held that the eighth amendment's bar against cruel and unusual punishment forbids the execution of persons under the age of eighteen. The defendant maintained that the reasoning of that case applied equally to the present case. In particular, the court in Roper had identified three characteristics that distinguish juvenile offenders from adult offenders: (1) immaturity and an underdeveloped sense of responsibility; (2) susceptibility to peer pressure and negative influences; and (3) transitory personality traits. Id., at 569-70, 125 S.Ct. 1183. The court explained that these characteristics "render suspect any conclusion that a juvenile falls among the worst offenders. The susceptibility of juveniles to immature and irresponsible behavior means their irresponsible conduct is not as morally reprehensible as that of an adult.... Their own vulnerability and comparative lack of control over their immediate surroundings mean juveniles have a greater claim than adults to be forgiven for failing to escape negative influence in their whole environment." (Citation omitted; internal quotation marks omitted.) Id., at 570, 125 S.Ct. 1183. The court further observed that, as a result of these characteristics, juveniles generally have "diminished culpability" for the crimes that they commit. Id., at 571, 125 S.Ct. 1183.
The trial court denied the defendant's motion to dismiss, explaining that the rationale and holding of Roper applied only to the imposition of the death penalty on juvenile offenders and not to the imposition of any other type of punishment on juveniles. Following a trial, the jury found the defendant guilty of the victim's murder. The defendant subsequently filed a motion for reconsideration of the court's denial of his motion to dismiss and for permission to supplement the record with scientific research relating to the cognitive and psychosocial development of adolescents. The trial court granted the motion, and the defendant filed a supplemental memorandum of law in which he again asserted that §§ 46b-127(a) and 53a-35a(2) violate the defendant's rights under the eighth amendment because, under Roper, subjecting juveniles to the same sentencing scheme as adults, without affording the trial judge discretion to impose a lesser sentence than the mandatory minimum prescribed for persons sixteen years or older, constitutes cruel and unusual punishment.
Prior to sentencing, the trial court conducted a hearing on the defendant's motion. At the hearing, defense counsel adduced testimony from Karen Howard Brody, a psychiatrist, regarding the development of the adolescent brain generally and the defendant's cognitive development in particular. According to Brody, new technologies have revealed significant differences between the adolescent brain and the adult brain, including differences in psychosocial functioning. Brody testified that adolescents are more readily influenced by their peers and have different attitudes toward risk and risk taking, with less orientation toward the future than adults. Brody, who had examined the defendant on three occasions, opined that he was a typical teenager who still exhibited methods of thinking characteristic of an adolescent. Brody further testified that, although the legal system considers a defendant's actions in light of what a reasonable person would do under the circumstances, in her view, an adolescent's actions should be measured against what a reasonable adolescent *776 would do under the circumstances.
Thereafter, the trial court denied the defendant's motion to dismiss. The trial court reiterated that Roper was inapplicable because it involved the constitutionality of the death penalty as applied to juveniles and did not implicate the constitutional rights of juveniles who, like the defendant in the present case, are sentenced to a term of imprisonment. The court further noted that the United States Supreme Court, in declaring the execution of juveniles unconstitutional in Roper, had approved a sentence of life imprisonment without the possibility of release for the juvenile defendant in that case. The trial court reasoned that if a life sentence without the possibility of release does not constitute cruel and unusual punishment, then the defendant's exposure in the present case to a mandatory minimum sentence of twenty-five years imprisonment cannot possibly violate the eighth amendment.
At the sentencing hearing, defense counsel urged the court to consider the defendant's age at the time of the offense as a mitigating factor. Defense counsel also requested that the court consider certain scientific studies that previously had been filed with the court in connection with the defendant's motion to dismiss and that supported the defendant's claim of "a biological basis" for diminished culpability in adolescents. Before imposing sentence, the trial court stated in relevant part: "[I]ntentional murder is the most serious crime we have on the books.... My job is to consider that crime, consider the impact on [the victim's family], and consider the fact you were fifteen years old. And I accept the psychiatrist's testimony that your judgment and your thinking was in development; and, maybe, if you were twenty-five and this thing happened again, you'd make a different choice. But that didn't happen. But I think it is appropriate to mitigate the sentence based on your age and the other information that your lawyer has presented to the court. But that only goes so far." The court subsequently sentenced the defendant to thirty-five years imprisonment. This appeal followed.
On appeal, the defendant renews his claim under Roper that, as § 53a-35a(2) applies to juveniles, the mandatory minimum sentence for murder prescribed therein violates the eighth amendment to the United States constitution. The defendant also claims that his right to a fair trial was violated when the state's attorney suggested in closing argument that the defendant had a motive for murdering the victim even though no evidence of motive had been presented during the trial.

I
We first address the defendant's claim, predicated on Roper, that §§ 46b-127(a) and 53a-35a(2) violate the defendant's right under the eighth amendment to be free from cruel and unusual punishment[9] insofar as those statutory provisions deprive the trial court of discretion to impose a sentence on a juvenile that is less than the mandatory minimum of twenty-five years imprisonment. The defendant contends that, although the mandatory minimum sentence reasonably may be applied to adult offenders, juveniles possess unique characteristics that render them relatively less culpable than adults, *777 and, consequently, the imposition of a mandatory minimum sentence on juveniles under §§ 46b-127(a) and 53a-35a(2) is unconstitutionally harsh.[10]
It is important to note at the outset what the defendant does not claim. The defendant does not contend that, in all cases, juveniles must be treated differently than adults for sentencing purposes, or that, as a general matter, juveniles cannot be held responsible for their crimes as if they were adults. The defendant also does not maintain that it is unconstitutional to sentence a juvenile to a term of imprisonment of thirty-five years for the crime of murder. On the contrary, the defendant recognizes that such claims are foreclosed by precedent both of the United States Supreme Court and of this court. The defendant's sole claim, rather, is that the eighth amendment bars a sentencing scheme that requires a mandatory minimum sentence without regard for the particular characteristics that distinguish juvenile offenders from adult offenders. In essence, the defendant claims that, under Roper, the imposition of a mandatory minimum prison term on a juvenile is constitutionally prohibited.
Subsequent to oral argument in the present case, this court, in State v. Allen, 289 Conn. 550, 580-81, 958 A.2d 1214 (2008), rejected a claim that a mandatory sentence of life imprisonment without the possibility of release for the crime of capital felony constitutes cruel and unusual punishment of a juvenile in light of Roper. In doing so, we explained that, "[i]n Roper, the United States Supreme Court held that execution of individuals who were under eighteen years of age at the time of their capital crimes violates the eighth amendment's prohibition against cruel and unusual punishment.... The scope of Roper, [however] is narrow: it applies only [when] an individual under eighteen years of age is sentenced to death.... Thus, the court in Roper recognized that the death penalty is different. Life without the possibility of release does not completely eliminate the possibility of rehabilitation; that possibility exists while the offender remains in prison." (Citations omitted; internal quotation marks omitted.) Id., at 581-82, 125 S.Ct. 1183.
In Allen, we also expressly adopted the reasoning of the Delaware Supreme Court, which, in Wallace v. State, 956 A.2d 630 (Del.2008), stated in relevant part: "Every state provides some mechanism for the imposition of adult sentences on a juvenile offender for at least some sort of crime. In other jurisdictions, there is no evident trend away from imposing serious adult *778 criminal liability [on] juvenile offenders.... [I]n forty-nine states, the age at which a first degree murderer can face adult disposition is fourteen years or younger. Forty-two states permit the sentencing of juveniles to life without parole. In twenty-seven of those states, the sentence is mandatory for anyone, child or adult, found guilty of [m]urder in the [f]irst [d]egree.... [I]n the past twenty years, courts have consistently rejected [e]ighth [a]mendment claims made by juvenile murderers attacking their life sentences.
"In Roper, the United States Supreme Court noted the `particular trend in recent years toward cracking down on juvenile crime.' However, in Roper, the United States Supreme Court concluded that `neither retribution nor deterrence provides adequate justification for imposing the death penalty on juvenile offenders.' The [United States] Supreme Court nevertheless also stated that it could not `deny or overlook the brutal crimes too many juvenile offenders have committed.' Consequently, it held that `when a juvenile offender commits a heinous crime, the [s]tate can exact forfeiture of some of the most basis liberties, but the [s]tate cannot extinguish his life and his potential to attain a mature understanding of his own humanity.'
"In Roper, the United States Supreme Court stated that `it is worth noting that the punishment of life imprisonment without the possibility of parole is itself a severe sanction, in particular for a young person.'" (Emphasis added.) Id., at 640-41. The Delaware Supreme Court concluded that "the United States Supreme Court, in Roper, would not have recognized a sentence of life without parole as an acceptable alternative to death as a punishment for juveniles who commit intentional [m]urder in the [f]irst [d]egree, if such a sentence would violate the [e]ighth [a]mendment." Id., at 641.
We concluded our analysis in Allen as follows: "The courts are in consensus ... that the United States Supreme Court clearly has signaled that ... a [mandatory life sentence for a person under the age of eighteen] does not violate the eighth amendment. The delineation between juveniles and adults for purposes of prosecution and punishment is a public policy determination reserved to the legislative branch of government, except [when] constitutional principles apply. The eighth amendment affords heightened significance to the `diminished culpability' of juveniles, but the reasoning of Roper does not extend to the present case." State v. Allen, supra, 289 Conn. at 585, 958 A.2d 1214.
Our reasoning and holding in Allen necessarily resolve the eighth amendment claim that the defendant raises in the present case: if, as we concluded in Allen, it is not cruel and unusual punishment to mandate a sentence of life imprisonment without the possibility of release in the case of an offender who is under the age of eighteen, a fortiori, it is not cruel and unusual punishment to mandate a sentence of not less than twenty-five years imprisonment in the present case. We therefore reject the defendant's constitutional claim.

II
The defendant next claims that the state's attorney engaged in improper closing argument, thereby depriving the defendant of a fair trial. Specifically, the defendant contends that the state's attorney suggested that the defendant had a motive for murdering the victim even though the state had failed to adduce any evidence of motive. Even if we assume, without deciding, that the challenged argument was improper, we conclude that any such impropriety was harmless beyond a reasonable doubt.
*779 The following additional facts are necessary to our disposition of this claim. In his initial argument to the jury, the state's attorney remarked as follows: "And finally, with respect to motive, as the court will tell you, the state does not have to prove motive. It's not an element of the crime. However, a lack of motive may cause you to have doubt about the case. A strong motive may cause you to feel it enhances the state's case. In this case, there [was] testimony of [Samuel] Redd with respect toand you remember them eyeing, looking at each other." At this point, defense counsel objected to the state's attorney's argument on the ground that, although evidence of Redd's motive for kicking in the victim's car window had been presented to the jury, no evidence of the defendant's motive for murdering the victim had been adduced. The trial court overruled the objection, stating that, "[i]f it's evidence in the case, each side can argue about the evidence.... [The state's attorney] is making his argument about... Redd's statement, and he's entitled to do that." Thereafter, the state's attorney continued: "In any event, it is true what [defense] counsel said; there is no evidence that her client had a motive. I'm going to ask you to look at all the circumstances, that they both happened to be out there that day. They both, according to [Ismail] Nasser, ran off together, and they knew each other. And it is correct that... Redd is the only one to say that he had heard that the victim ... had fired shots in the neighborhood. And if you believe that the accused is the one who fired the shots, it was obviously a motive because you can reasonably assume that people just don't walk around shooting other people in cars unless there is a motive. So motive isn't an element that has to be proven. It may help or it may hurt by way of its existence or its nonexistence."[11]
Our jurisprudence concerning prosecutorial impropriety during closing argument is well established. "[I]n analyzing claims of prosecutorial [impropriety], we engage in a two step analytical process. The two steps are separate and distinct: (1) whether [impropriety] occurred in the first instance; and (2) whether that [impropriety] deprived a defendant of his due process right to a fair trial. Put differently, [impropriety] is [impropriety], regardless of its ultimate effect on the fairness of the trial; whether that [impropriety] caused or contributed to a due process violation is a separate and distinct question.... [O]ur determination of whether any improper conduct by the state's attorney violated the defendant's fair trial rights is predicated on the factors set forth in State v. Williams, [204 Conn. 523, 540, 529 A.2d 653 (1987)], with due consideration of whether that [impropriety] was objected to at trial." (Internal quotation marks omitted.) State v. Warholic, 278 Conn. 354, 361-62, 897 A.2d 569 (2006). "These factors include the extent to which the [impropriety] was invited by defense conduct or argument, the severity of the [impropriety], the frequency of the [impropriety], the centrality of the [impropriety] to the critical issues in the case, the strength of the curative measures adopted, and the strength of the state's case." Id., at 361, 897 A.2d 569.
"A prosecutor may invite the jury to draw reasonable inferences from *780 the evidence; however, he or she may not invite sheer speculation unconnected to evidence.... Moreover, when a prosecutor suggests a fact not in evidence, there is a risk that the jury may conclude that he or she has independent knowledge of facts that could not be presented to the jury." (Citations omitted.) State v. Singh, 259 Conn. 693, 718, 793 A.2d 226 (2002).
We conclude that the state's attorney's suggestion during closing argument that the defendant and Redd shared a common motive for committing their respective crimes against the victim bordered on the speculative because any link between the conduct of the two men was weak at best. Indeed, there was no direct evidence to support the state's attorney's argument, and it is debatable whether the circumstantial evidence was sufficient to warrant the inference of motive that the state's attorney advocated. We need not decide, however, whether the state's attorney's comments rose to the level of impropriety because, even if they were improper, we conclude that they were harmless.
This court recently considered a similar claim of prosecutorial impropriety in State v. Grant, 286 Conn. 499, 944 A.2d 947, cert. denied, ___ U.S. ___, 129 S.Ct. 271, 172 L.Ed.2d 200 (2008). The defendant, Edward Grant, murdered his victim in a parking garage in New Haven and then drove away in the victim's vehicle. See id., at 503-504, 540, 944 A.2d 947. Immediately thereafter, he abandoned the vehicle on another level of the parking garage. See id., at 504, 540, 944 A.2d 947. During trial, no evidence of Grant's motive for killing the victim was adduced. See id., at 540, 944 A.2d 947. In the prosecutor's closing argument, he acknowledged that the jury did not "have any direct evidence of ... the motive for this crime." (Internal quotation marks omitted.) Id., at 540, 944 A.2d 947. Defense counsel, in his closing argument, contended that the absence of any evidence of motive "gave rise to a reasonable doubt about [Grant's] guilt." Id. On rebuttal, the prosecutor indicated that the reason Grant had killed the victim was to steal her vehicle. See id., at 540-41, 944 A.2d 947. The prosecutor also conceded, however, that, in light of the nature of the available circumstantial evidence, there was "not a clear answer" to the question of motive. (Internal quotation marks omitted.) Id., at 541, 944 A.2d 947.
In rejecting Grant's claim that the prosecutor's comments constituted harmful error, we explained: "First, the prosecutor... acknowledged to the jury that there was no direct evidence of motive, thereby reducing the impact of any impropriety. Second, the prosecutor did not suggest that there were facts not in evidence that would support a finding of motive but relied entirely on the evidence that [Grant] had driven the [vehicle] in support of his argument. Thus, the weakness of the inference suggested by the prosecutor was readily discernible to the jury. Finally, the remark was isolated and was not central to the state's case." Id., at 542, 944 A.2d 947.
Likewise, in the present case, the state's attorney underscored the fact that there was no direct evidence of the defendant's motive for killing the victim. The state's attorney also did not suggest that he was aware of facts not in evidence that would support a finding of motive; rather, he relied solely on Redd's testimony that Redd and the defendant knew each other from the neighborhood and that he, Redd, had harbored ill will toward the victim because of a shooting incident in his neighborhood. Thus, the jury was aware that the state's attorney's argument was supported by a weak factual foundation.[12] Finally, *781 as in Grant, the state's attorney's argument was not central to the state's case, which was predicated primarily on L.C.'s eyewitness identification of the defendant as the killer. We conclude, therefore, that the state's attorney's allegedly improper argument was harmless and did not deprive the defendant of a fair trial.
The judgment is affirmed.
In this opinion the other justices concurred.
NOTES
[1]  General Statutes § 53a-54a provides in relevant part: "(a) A person is guilty of murder when, with intent to cause the death of another person, he causes the death of such person...."

Murder is punishable as a class A felony. See General Statutes § 53a-54a(c).
[2]  General Statutes (Rev. to 2003) § 46b-127 provides in relevant part: "(a) The court shall automatically transfer from the docket for juvenile matters to the regular criminal docket of the Superior Court the case of any child charged with the commission of a capital felony, a class A or B felony or a violation of section 53a-54d, provided such offense was committed after such child attained the age of fourteen years and counsel has been appointed for such child if such child is indigent....

"(c) Upon the effectuation of the transfer, such child shall stand trial and be sentenced, if convicted, as if he were sixteen years of age...." All references in this opinion to § 46b-127 are to the revision of 2003.
[3]  The defendant also was charged with and convicted of carrying a pistol without a permit in violation of General Statutes § 29-35. The defendant's conviction for that offense is not a subject of this appeal.
[4]  General Statutes § 53a-35a provides in relevant part: "For any felony committed on or after July 1, 1981, the sentence of imprisonment shall be a definite sentence and the term shall be fixed by the court as follows ... (2) for the class A felony of murder, a term not less than twenty-five years nor more than life...."
[5]  The defendant was sentenced to a concurrent five year term of imprisonment for his conviction of carrying a pistol without a permit. See footnote 3 of this opinion. Thus, the defendant's total effective sentence was thirty-five years imprisonment.
[6]  The defendant appealed directly to this court pursuant to General Statutes § 51-199(b), which provides in relevant part: "The following matters shall be taken directly to the Supreme Court . . . (3) an appeal in any criminal action involving a conviction for a. . . class A felony...."
[7]  The eighth amendment to the United States constitution provides: "Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted."

The eighth amendment's prohibition against cruel and unusual punishment is made applicable to the states through the due process clause of the fourteenth amendment to the United States constitution. See, e.g., Tuilaepa v. California, 512 U.S. 967, 970, 114 S.Ct. 2630, 129 L.Ed.2d 750 (1994).
[8]  We refer to L.C., a juvenile, by his initials to protect his privacy interests.
[9]  It is well established that "[c]ruel and unusual punishment encompasses more than barbarous physical punishment.... It also includes punishments which involve the unnecessary and wanton infliction of pain ... and those which are grossly disproportionate to the severity of the crime." (Citations omitted.) Arey v. Warden, 187 Conn. 324, 328, 445 A.2d 916 (1982).
[10]  We note, preliminarily, that the state contends that the defendant's claim is not reviewable because it poses a purely academic question. In particular, the state maintains that, because the trial court sentenced the defendant to a term of imprisonment in excess of the twenty-five year mandatory minimum and did not otherwise indicate that, if authorized to do so, it would have sentenced the defendant to a prison term of less than twenty-five years, there is no reason to believe that the statutory minimum affected the thirty-five year sentence that the court imposed. It is true, of course, as the state contends, that this court does not render advisory opinions, and, therefore, we will not entertain an appeal when the question presented is purely academic. See, e.g., Pasquariello v. Stop & Shop Cos., 281 Conn. 656, 664 n. 8, 916 A.2d 803 (2007). On the basis of the record presented, however, we simply do not know whether the minimum sentence required under our statutory scheme affected the sentence that the trial court actually imposed on the defendant. Moreover, the trial court was under no obligation to explain whether it might have imposed a more lenient sentence and, if so, what that sentence might have been, if it had not been statutorily required to impose a minimum prison term of twenty-five years. In such circumstances, we cannot say that the defendant's claim regarding the constitutionality of §§ 46b-127(a) and 53a-35a(2) as applied to juveniles is merely academic.
[11]  Defense counsel responded in her closing argument in relevant part: "In addition to the inconsistencies I've pointed out to you, there is no evidence at all in this case that [the defendant] had any motive to kill [the victim]. There's not even any evidence that he knew him. You heard about motive. You heard about ... Redd's motive to hurt [the victim]. [The state's attorney] somehow wants you to transfer . . . Redd's motives to my client. But you just can't do that, and I know you won't do that."
[12]  In addition, in her closing argument, defense counsel emphasized this weakness in the probative force of this portion of the state's attorney's closing argument. See footnote 11 of this opinion.
