878 F.2d 608
28 Fed. R. Evid. Serv. 658
UNITED STATES of America, Appellee,v.Alfredo DIAZ, Eradio Perez, and Jose Alfanso Riano,Defendants-Appellants.
Nos. 1134, 1260 and 1261, Dockets 87-1462, 87-1463 and 87-1464.
United States Court of Appeals,Second Circuit.
Argued June 8, 1988.Decided June 29, 1989.

Debra D. Newman, Asst. U.S. Atty. for the E.D.N.Y., Brooklyn, N.Y.  (Andrew J. Maloney, U.S. Atty. for the E.D.N.Y., Emily Berger, David C. James, Asst. U.S. Attys., Brooklyn, N.Y., of counsel), for appellee.
Barry E. Schulman, Brooklyn, N.Y.  (Michael A. O'Connor, Doreen T. O'Connor, Schulman & Laifer, Brooklyn, N.Y., of counsel), for defendants-appellants Eradio Perez and Jose Alfanso Riano.
Joel B. Rudin, New York City (Mass & Rudin, of counsel), for defendant-appellant Alfredo Diaz.
Before VAN GRAAFEILAND and MAHONEY, Circuit Judges, and NEVAS,* District Judge.
MAHONEY, Circuit Judge:


1
Appeal from judgments of conviction entered in the United States District Court for the Eastern District of New York, Nicholas J. Tsoucalas, Judge, United States Court of International Trade, sitting by designation, after a jury trial of a one-count indictment charging defendants-appellants with conspiracy to possess with intent to distribute cocaine in violation of 21 U.S.C. Secs. 841(a)(1) and 846 (1982).  Defendants-appellants raise numerous issues on appeal.  We consider herein their contentions that:  (1) the district court erroneously admitted evidence concerning prior events allegedly probative of the charged conspiracy which was inflammatory, prejudicial and unconnected to defendants;  (2) the district court erroneously admitted certain expert opinion testimony of agents of the Drug Enforcement Administration ("DEA");  and (3) in any event, the evidence was insufficient to sustain their convictions because it failed to establish defendants' knowing participation in a cocaine conspiracy.


2
Affirmed.

Background

3
The defendants were arrested on May 7, 1987.  They claim error in the admission of evidence pertaining to certain events prior to that date.  We shall therefore consider:  (1) events prior to May 7, 1987;  (2) the events of that day;  and (3) certain aspects of the conduct of the trial.  In view of the jury's verdict, we view the evidence in the light most favorable to the government, and all permissible inferences are construed in its favor.  See, e.g., United States v. Chang An-Lo, 851 F.2d 547, 554 (2d Cir.), cert. denied, --- U.S. ----, 109 S.Ct. 493, 102 L.Ed.2d 530 (1988);  United States v. Grubczak, 793 F.2d 458, 463 (2d Cir.1986);  United States v. Nersesian, 824 F.2d 1294, 1324 (2d Cir.), cert. denied, --- U.S. ----, 108 S.Ct. 355, 98 L.Ed.2d 380 (1987).


4
A. Events Prior to May 7, 1989.


5
On February 20, 1987, DEA agents Michael Torretta and Raymond Mansolillo observed two men using a beeper at a public telephone on the corner of 47th Avenue and 195th Street in Queens, New York, New York (the "Phone").  The men looked at their beeper and then dialed a telephone number on the Phone, hung up and then received a return call.  The interest of the agents was aroused because they were aware that narcotics traffickers commonly use beepers in conjunction with public telephones.


6
After concluding the telephone call, the men got into a car parked nearby and drove away, with the agents following.  After proceeding approximately two blocks, the two men stopped their car, transferred two white plastic bags from the interior of their car to the trunk, and drove away.  They then drove for approximately five blocks, squaring blocks.  The agents then stopped the car.


7
Torretta and Mansolillo approached the car, identified themselves as DEA agents, and asked to search the trunk of the car.  When one of the men opened the trunk in response to the agents' request, Torretta and Mansolillo discovered five kilograms of cocaine packaged in white plastic bags.  The two men were then arrested.


8
Following this event, Agent Torretta continued periodic surveillance of the Phone.  On April 1, 1987, Agent Torretta again saw two men placing beeper calls at the Phone.  The two men then went to a nearby car and drove away.  Agent Torretta followed them.  They drove directly to a single family residence located at 46-18 190th Street, Queens (the "House"), less than three blocks away from the location where the February 20 arrest took place, and further in the direction in which the vehicle had been headed when stopped on February 20.  Agent Torretta watched the two men enter the House and leave about forty-five minutes later carrying two white plastic bags which were filled with some unknown contents.


9
The two men placed the bags in the trunk of their car and drove to another nearby public telephone, with Agent Torretta still following.  When they arrived at this phone, Agent Torretta saw a second car meet the car that he was following, but was unable to keep the two cars continually in view while he moved his vehicle into position to maintain his surveillance.  When Torretta resumed his surveillance, he saw the two cars drive away separately.


10
Agent Torretta, now joined by Agent Mansolillo whom he had summoned for assistance, followed the car occupied by the two men who had carried the bags out of the House, and eventually halted that car.  Upon request, the two men opened the trunk of the car, revealing that the two plastic bags they had earlier placed therein had been removed.


11
As a result of the events of April 1, DEA agents commenced conducting surveillance of the House.  During that surveillance, in the latter part of April, 1987, Agent Mansolillo observed two men leave the House, proceed to the Phone, place a phone call, and return to the House.


12
B. The Events of May 7, 1987.


13
On the morning of May 7, 1987, Agents Torretta and Mansolillo were interviewing neighbors of the House in connection with their surveillance of that site.  During the course of one interview, they noticed three men, later identified as the defendants, in a gray Chevrolet automobile that pulled up in front of the House.  Upon noticing the agents looking at them, however, defendants drove on.  The agents attempted unsuccessfully to follow them in the agents' own vehicle, which they then parked about a half block from the House.  As they did so, they observed defendants returning to the House in the Chevrolet.


14
Diaz and Perez got out of the car and headed toward the House.  Perez entered the House while Diaz stood on the front porch with an unidentified male.  Riano remained by the car, opening its hood, appearing to the agents to be functioning as a lookout.  Perez then came out of the house carrying a large cardboard box, which he placed in the trunk of the Chevrolet.  Riano and Perez drove away in the Chevrolet, leaving Diaz behind.


15
Agents Torretta and Mansolillo followed Riano and Perez, who drove the Chevrolet in what the agents deemed to be a "surveillance conscious" manner, squaring blocks, travelling east and west on the same roads, and generally driving "around in circles."    Riano finally parked the Chevrolet adjacent to the Cue Variety Store, located on Roosevelt Avenue, just west of Union Street, in Queens.  Riano and Perez then entered the store.  The agents called for assistance, and DEA agents Fred Geiger and Arthur Kerse joined the surveillance.  For most of the next hour and a half, Riano and Perez remained in the Cue Variety Store.  Various males came out of the store from time to time and looked up and down the street, appearing to the agents to be functioning as lookouts.


16
Riano and Perez then left the store and entered a card shop in the neighborhood.  A few minutes later, the two men left the card shop, made a call on a public telephone, and walked to a nearby municipal parking lot on Union Street.  Riano and Perez were joined there by another individual, who helped them jump start a gray Buick.  Riano and Perez then departed in the Buick, with Torretta and Mansolillo following behind.  Shortly thereafter, Riano and Perez were apprehended and arrested.


17
An ensuing search of the gray Chevrolet left in front of the Cue Variety Store discovered over $1,000,000 in cash contained in the cardboard box that earlier had been placed in the car's trunk outside the House.  In addition, the DEA agents found in the Chevrolet's glove compartment a U.S. Customs receipt dated December 16, 1986 for a tractor trailer truck and $999,960 in United States currency (the "Customs Receipt").


18
In the meantime, Agent Gerald McAleer, who had been summoned to the 190th Street surveillance location, observed the activities of Diaz, who had remained at the House.  McAleer saw Diaz leave the House carrying two large plastic bags.  Diaz carried the bags to a parked car several blocks away.  While Diaz was attempting to place the bags in the trunk of the car, McAleer approached Diaz and identified himself as a DEA agent.  When McAleer looked into the opened plastic bags, he noticed in plain view a large amount of cash, later determined to be approximately $28,000 in small denominations.  McAleer immediately placed Diaz under arrest, at which time McAleer discovered an additional $30,000 in $100 bills in the breast pocket of Diaz's jacket.


19
In addition, index cards were seized from Diaz with writing thereon which a government expert testified could constitute the calculation of broker's fees for sales of cocaine.  A search was made of the House, resulting in the recovery of a red ledger which, according to the same government expert, apparently contained records of cocaine sales.  The search also recovered a laboratory mask, protective gloves, plastic bags and tape, but neither that search nor a subsequent vacuum sweep of the House revealed any trace of cocaine.  When Riano and Perez were arrested, the agents found in the Buick a roll of tape of the same color and brand as the tape used on the box recovered from the Chevrolet containing $1,000,000, and the tape found in the House.  In addition, Riano had on his person the most recent Consolidated Edison utility bill for the House addressed to "Francisco Rodriquez," the lessee.


20
C. The Trial.


21
At trial, the government successfully contended that the House was a cocaine-related money "stash pad" for the charged conspiracy.1   It was able to do so through the testimony of the owner of the House, three neighbors and the local mailman, in addition to the testimony of the DEA agents involved.


22
The landlord and owner of the house, Ker Chang, testified that in October, 1986, he rented the home to one Francisco Rodriguez for a one-year term.  The lease required a rent of $1,300 to be paid on the 25th day of each month.  It was Chang's practice personally to collect the rent at the House on the appropriate day.  The rent was always paid in cash.  He observed that there was no telephone in the House.  In November and December, 1986, a lady paid the rent.  Commencing in January, 1987, Chang collected the rent from a group of men, and there was less furniture in the House.  On April 25, 1987, no one was in the House to pay the rent, so Chang returned the following day and, again finding nobody there, entered the House and ascertained that more furniture had been removed.


23
The neighbors testified that they had noticed several unusual things about the House and its occupants.  Groups of men would arrive at the house, stay for short periods of time, and then leave.  On occasion, the men would transport plastic garbage bags in and out of the House, on one occasion throwing bags out of a dining room window into a van parked in the driveway.  Mattresses were also carried in and out of the House.  Lights were left on in the House continuously.  One neighbor reported that a "strange odor" had emanated from the basement of the House on two occasions.  Finally, the local mailman stated that the occupants received utility bills and junk mail, but no personal correspondence or magazines.


24
Various DEA agents testified to the events preceding May 7, 1987 previously described herein, and the events of that day, as well as to the characteristics of the House and its occupants also described by the testifying neighbors and postman.


25
Defendants moved in limine to bar any testimony concerning the events prior to May 7, 1987, and objected continuously to that evidence as it was introduced in the course of the trial.  The district court rejected the pretrial motion "at this time," pending trial developments.  When testimony concerning the cocaine seizure of February 20, 1987 was first tendered, the court allowed it, but stated that "if it's not connected it's going to be stricken at the end."    At the conclusion of the government's case, the court denied motions by the defense to acquit and to strike the testimony concerning the pre-May 7 events, observing as to the latter:  "The motion is denied since this is a conspiracy."    Although the matter was thereafter raised by the defense on several occasions, the court did not change its ruling.  The defense also objected unavailingly to the introduction of the Customs Receipt.


26
DEA agent Richard McCarthy testified as an expert witness concerning the financial aspects of drug operations.  He described the red ledger found in the House as appearing to list the dates of drug transactions (culminating on May 7, 1987, the day the ledger was seized), the first name of the distributor, the amount of money paid, and the amount of money still due and owing.  Another page of entries was described as reflective of a money count "commonly found in stash pads."    Agent McCarthy testified that certain index cards seized from defendant Diaz appeared to detail brokerage commissions on cocaine transactions.


27
Riano and Perez presented an alibi defense, contending that they were at the immigration office at 26 Federal Plaza in Manhattan applying for an extension of stay for Riano at the time the DEA agents testified Riano and Perez were at the House on May 7, 1987.  Riano and Perez presented their alibi through three defense witnesses, but did not themselves testify.


28
Diaz called no witnesses and did not testify.  The jury rendered a verdict of guilty against all defendants.  Diaz was sentenced to a fifteen-year term of imprisonment and a fifty dollar special assessment.  Perez and Riano were each sentenced to terms of twenty years imprisonment and a fifty dollar special assessment.  This appeal ensued.  Defendants are presently serving their sentences.

Discussion

29
Defendants press numerous contentions on appeal.  As indicated earlier, we consider in detail their claims that:  (1) the district court erroneously admitted evidence concerning prior events allegedly probative of the charged conspiracy which was inflammatory, prejudicial and unconnected to defendants;  (2) the district court erroneously admitted certain opinion testimony of agents of the DEA;  and (3) in any event, the evidence was insufficient to sustain their convictions because it failed to establish defendants' knowing participation in a cocaine conspiracy.


30
A. Admission of Evidence Concerning Prior Events.


31
Defendants object to the admission of testimony by DEA agents concerning the cocaine seizure of February 20, 1987 and the subsequent events of April 1, 1987 involving the House and the Phone.  Although the logic of their position would call for objection to Agent Mansolillo's testimony concerning the incident in the latter part of April, as well, this matter is not addressed by defendants.  Finally, defendants object to the admission of the Customs Receipt.


32
We note at the outset that "determinations of relevance are entrusted to the sound discretion of the trial judge, and his decision will not be overturned unless he has acted arbitrarily or irrationally."    United States v. Cruz, 797 F.2d 90, 95 (2d Cir.1986) (citing O'Rourke v. Eastern Airlines, 730 F.2d 842, 854 (2d Cir.1984)).


33
Rule 401 of the Federal Rules of Evidence defines relevant evidence as evidence "having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence."    Fed.R.Evid. 401.  "Implicit in that definition are two distinct requirements:  (1) [t]he evidence must be probative of the proposition it is offered to prove, and (2) the proposition to be proved must be one that is of consequence to the determination of the action."    United States v. Hall, 653 F.2d 1002, 1005 (5th Cir.1981).  Of course, evidence must be relevant to be admissible.  See Fed.R.Evid. 402.


34
We shall consider first the evidence of the cocaine seizure on February 20, 1987.  Defendants' challenge is directed at the second requirement cited above, which they claim the government has failed to meet.  Defendants contend that what is proved by the evidence of the February 20 seizure cannot possibly be of consequence to the events of May 7, 1987 and the conspiracy charged in the indictment.


35
The government claims, on the other hand, that there are at least four reasons that would allow a jury to infer a rational connection:  (1) the proximity of the seizure of the cocaine to the House in a low density, residential neighborhood;  (2) the odds against having two multi-kilogram cocaine operations occurring within a narrow radius around the House in this residential area;  (3) the use of the same public telephone used by other persons connected with the House, despite the fact that there was a public telephone closer to the House;  and (4) the packaging of the cocaine in the same containers--white plastic garbage bags--that were used by Diaz to transport the money he removed from the House as well as by other users of the House, including the men stopped on April 1, 1987.


36
The district court initially allowed introduction of this evidence subject to later connection.  Standing alone, of course, there was nothing but speculation to connect the February 20 cocaine seizure to the House.  The evidence of subsequent events, however, sufficed in our view to render the admission of this evidence a permissible exercise of the district court's discretion.


37
Specifically, on April 1, 1987, two men made a beeper call at the Phone;  departed in the same direction as the February 20 users of the Phone but, uninterrupted by the authorities, continued to the House;  and left the House forty-five minutes later carrying "weighted" white plastic bags which they placed in the trunk of their car.  Later in April, occupants of the House were observed to proceed from the House to the Phone, make a telephone call, and return to the House, which had no telephone.


38
These later events provided a basis to infer a connection between the House, the Phone, and a cocaine conspiracy that utilized the House and the Phone in the course of its operations.  In that light, the district court could properly conclude, in the exercise of its discretion, that evidence concerning the events of February 20, 19872 had "any tendency" to make "more probable," within the meaning of Fed.R.Evid. 401, the fact that the House was used as a money stash pad for a cocaine operation.  The evidence is obviously subject to attack, which defendants did most vigorously at trial and here.  For example, one could question whether the two men arrested on February 20, 1987 would in fact have proceeded to the House if they had not been apprehended, or challenge the inference that the white plastic bags removed from the House on April 1, 1987 contained cocaine, money, or anything else probative of or connected with a cocaine conspiracy.  Once relevance is established, however, such challenges go to weight rather than admissibility.  See United States v. Viserto, 596 F.2d 531, 536 (2d Cir.)  (relevance of evidence "not so far-fetched as to make its admission an abuse of discretion"), cert. denied, 444 U.S. 841, 100 S.Ct. 80, 62 L.Ed.2d 52 (1979);  cf. Loughan v. Firestone Tire & Rubber Co., 749 F.2d 1519, 1523 (11th Cir.1985) (conflicting testimony goes to weight of evidence and not admissibility);  Carter v. Massey-Ferguson, Inc., 716 F.2d 344, 348 (5th Cir.1983) (evidence need not be dispositive of an issue to be relevant) (citing Fed.R.Evid. 401 advisory note).


39
We take a similar view of the events of April 1, 1987, and the incident later in April when two men were observed to go from the House to the Phone, make a telephone call, and return to the House.  Because of the direct connection of these events to the House, their admissibility follows a fortiori from our conclusion concerning the events of February 20.  Although evidence of these occurrences would not be admissible standing alone, the connections established between these various incidents, and the resulting overall context, suffice to establish admissibility.  See, e.g., 1 J. Weinstein & M. Berger, Weinstein's Evidence p 401, at 401-57 to 401-59 (1986).


40
Nor do we regard this evidence as unduly prejudicial, precluding admissibility under Fed.R.Evid. 403.  This rule allows the exclusion of evidence whose "probative value is substantially outweighed by the danger of unfair prejudice."    Id. (emphasis added).  " 'Unfair prejudice' within [Rule 403's] context means an undue tendency to suggest decision on an improper basis, commonly, though not necessarily, an emotional one."    Fed.R.Evid. 403 advisory committee's note.  The "logical inferences" resulting from proffered evidence do not engender the "unfair prejudice" against which Rule 403 is directed.  United States v. Dazzo, 672 F.2d 284, 288 (2d Cir.), cert. denied, 459 U.S. 836, 103 S.Ct. 81, 74 L.Ed.2d 77 (1982);  United States v. Sugar, 606 F.Supp. 1134, 1152 (S.D.N.Y.1985).  Defendants' substantial objection here pertains to the probative value of the challenged government evidence.  Rule 403 does not provide an independent basis for defendants' challenge to this evidence.


41
Finally, we see no error in the admission of the Customs Receipt, which evidenced a prior seizure of a tractor trailer truck and $999,960 in United States currency.  Defendants contend that the admission of this evidence violated Fed.R.Evid. 404(b), which precludes the admission of "[e]vidence of other crimes, wrongs or acts ... to prove the character of a person in order to show action in conformity therewith."    The rule goes on to say, however, that such evidence "may ... be admissible for other purposes, such as proof of motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident."    Id.  Furthermore:


42
Under the "inclusionary" approach followed in this circuit, "evidence of prior crimes, wrongs, or acts is admissible for any purpose other than to show a defendant's criminal propensity," United States v. Harris, 733 F.2d 994, 1006 (2d Cir.1984), as long as it is "relevant to some disputed issue in the trial" and satisfies the probative-prejudice balancing test of Fed.R.Evid. 403.  United States v. Figueroa, 618 F.2d 934, 939 (2d Cir.1980).  The trial judge has broad discretion to admit "other crimes" evidence under Rule 404(b), and he will not be overturned on appeal absent abuse of discretion.  Harris, 733 F.2d at 1006-07.    "Other crimes" evidence may be admitted to complete the story of the crimes charged.


43
United States v. Brennan, 798 F.2d 581, 589 (2d Cir.1986);  see also United States v. Ortiz, 857 F.2d 900, 903 (2d Cir.1988), cert. denied, --- U.S. ----, 109 S.Ct. 1352, 103 L.Ed.2d 820 (1989).


44
In this conspiracy case, evidence of crimes, wrongs or acts by coconspirators is admissible, see United States v. Salazar, 485 F.2d 1272, 1276 (2d Cir.1973), cert. denied, 415 U.S. 985, 94 S.Ct. 1579, 39 L.Ed.2d 882 (1974), and such proof ordinarily does not raise any Rule 404(b) question, see United States v. Bates, 600 F.2d 505, 509 (5th Cir.1979);  22 C. Wright & K. Graham, Federal Practice and Procedure Sec. 5239, at 451 (1978).  Furthermore, defendants objected to the introduction of the Customs Receipt at trial only on grounds of relevance, and raise their Rule 404(b) objection for the first time on appeal.  Fed.R.Evid. 103(a) provides in pertinent part, however, that:


45
Error may not be predicated upon a ruling which admits or excludes evidence unless a substantial right of the party is affected, and


46
(1) Objection.  In case the ruling is one admitting evidence, a timely objection or motion to strike appears of record, stating the specific ground of objection, if the specific ground was not apparent from the context....


47
Id.  (emphasis added).


48
Accordingly, we will only review the ruling of the district court on the ground of relevance presented below.  See United States v. Houser, 804 F.2d 565, 570 (9th Cir.1986);  United States v. Kanovsky, 618 F.2d 229, 231 (2d Cir.1980);  United States v. Rubin, 609 F.2d 51, 62 (2d Cir.1979), aff'd, 449 U.S. 424, 101 S.Ct. 698, 66 L.Ed.2d 633 (1981).3   The theory of the government's case was that the House was a money stash pad for a cocaine conspiracy, and the indictment charged that "[i]t was ... part of said conspiracy that the defendants and others would possess and conceal the cash proceeds of the conspiracy."    We have little trouble concluding that the Customs Receipt evidencing the recent seizure of $999,960, found in the glove compartment of a vehicle in which all the defendants drove to the House on the morning of May 7, 1987 and Perez and Riano departed with $1,000,000 in cash, was relevant to the offense charged within the meaning of Fed.R.Evid. 401.  Nor does the fact that the date of the Customs Receipt, December 16, 1986, precedes the date of the inception of the conspiracy charged in the indictment, March 1, 1987, preclude admission.  See supra note 2.


49
B. Admission of Opinion Testimony.


50
Defendants contend that the district court erred in admitting virtually all of Agent McCarthy's expert testimony and any opinion testimony offered by Agents Mansolillo and Torretta.  Specifically, defendants claim that these agents were improperly allowed to give testimony which went to ultimate issues in the case.  This contention is without merit.


51
The rules governing the admission of expert testimony in narcotics cases are well settled.  "Whether to receive or exclude expert testimony is, under long-standing law, a matter confided to the sound discretion of the trial court, which will not be reversed unless an appellate court can say that the ruling is 'manifestly erroneous.' "    United States v. Everett, 825 F.2d 658, 662 (2d Cir.1987) (quoting Spring Co. v. Edgar, 99 U.S. 645, 658, 25 L.Ed. 487 (1878)), cert. denied, --- U.S. ----, 108 S.Ct. 1035, 98 L.Ed.2d 999 (1988);  see United States v. Daly, 842 F.2d 1380, 1387-88 (2d Cir.), cert. denied, --- U.S. ----, 109 S.Ct. 66, 102 L.Ed.2d 43 (1988).


52
We applied this rule in the narcotics area in United States v. Nersesian, 824 F.2d 1294 (2d Cir.), cert. denied, --- U.S. ----, 108 S.Ct. 355, 98 L.Ed.2d 380 (1987), where we said:[I]t is well established that the operations of narcotics dealers are a proper subject for expert testimony under Fed.R.Evid. 702.  [United States v. Cruz, 797 F.2d 90, 96 (2d Cir.1986).]    In the past, we have upheld the admission of expert testimony to explain the use of narcotics codes and jargon in intercepted conversations.  E.g., United States v. Ginsberg, 758 F.2d 823, 830 (2d Cir.1985);  United States v. Cirillo, 499 F.2d 872, 881 (2d Cir.), cert. denied, 419 U.S. 1056, 95 S.Ct. 638, 42 L.Ed.2d 653 (1974).  We acknowledge some degree of discomfiture in cases such as the instant one in which this practice is employed, since, uncontrolled, such use of expert testimony may have the effect of providing the government with an additional summation by having the expert interpret the evidence.  See United States v. Brown, 776 F.2d 397, 401 (2d Cir.1985), cert. denied, [475 U.S. 1141,] 106 S.Ct. 1793, 90 L.Ed.2d 339 (1986).  In fact, in this case, the district judge recognized the danger that an expert may come dangerously close to usurping the jury's function.  Nevertheless, a district court's decision to allow an expert to testify will not be overturned lightly.


53
Id. at 1308.


54
Both in Brown, 776 F.2d at 401, and in Judge Newman's concurring opinion in United States v. Young, 745 F.2d 733, 765-66 (2d Cir.1984) (Newman, J., concurring), cert. denied, 470 U.S. 1084, 105 S.Ct. 1842, 85 L.Ed.2d 142 (1985), cited with approval in Brown, 776 F.2d at 401 & n. 6, we professed concern about allowing expert witnesses to provide outright characterizations of the role of individual defendants in narcotics transactions.  Nonetheless, in United States v. Scop, 846 F.2d 135 (2d Cir.), rev'd in part on rehearing, 856 F.2d 5 (2d Cir.1988), we summarized the holdings in Brown and Young, as well as in United States v. Carson, 702 F.2d 351, 369-70 (2d Cir.), cert. denied, 462 U.S. 1108, 103 S.Ct. 2456, 2457, 77 L.Ed.2d 1335 (1983), as follows:


55
In United States v. Carson, ... two Drug Enforcement Agency agents were allowed to testify concerning their opinion that conduct they observed involved a narcotics transaction.  Because "the clandestine manner in which drugs are bought and sold[ ] is unlikely to be within the knowledge of the average layman," id., the conclusions of the agents based on their years of experience were held admissible under Rule 702.  In United States v. Young, 745 F.2d 733, 760-61 (2d Cir.1984), cert. denied, 470 U.S. 1084, 105 S.Ct. 1842, 85 L.Ed.2d 142 (1985), a police detective was allowed to testify, based on his observations, that he believed a narcotics transaction had taken place.  In the same case, a DEA agent testifying as an expert witness was permitted to describe a typical chain of heroin distribution, including the characteristics and operating methods of a heroin "mill."    The district judge instructed the jury that this general description was unrelated to the facts or circumstances of the particular case.  The agent was then allowed to testify that what he found in defendant's apartment was precisely what he would have expected to find in a heroin "mill."    Id. at 761.    In United States v. Brown, 776 F.2d 397, 400 (2d Cir.1985), cert. denied, 475 U.S. 1141, 106 S.Ct. 1793, 90 L.Ed.2d 339 (1986), a police officer testifying as an expert was permitted to describe a typical drug buy in Harlem, including the role of the "steerer."    He was then permitted to testify over objection that the defendant acted as a "steerer" in a transaction the officer had observed.


56
In each of these cases, we upheld the convictions.  We noted in Brown, however, that "there is something rather offensive in allowing an investigating officer to testify not simply that a certain pattern of conduct is often found in narcotics cases, leaving it for the jury to determine whether the defendant's conduct fits the pattern, but also that such conduct fitted the pattern."    Id. at 401.    Nevertheless, the Advisory Committee's Note to Rule 704 cautions against limiting experts to "might or could" formulations when they are prepared to say "did," and Carson, Young and Brown appear to be consistent with that admonition.  Whether these results are desirable is not for us to say in light of the Rules' generally liberated approach to expert testimony.


57
Scop, 846 F.2d at 141-42;  see United States v. Hernandez, 862 F.2d 17, 24 n. 3 (2d Cir.1988) (approving testimony of "two government agents that clarified and interpreted drug records" as "clearly of a factual nature"), cert. denied, --- U.S. ----, 109 S.Ct. 1170, 103 L.Ed.2d 228 (1989).


58
Measured against these standards, we see no error in the district court's admission of the testimony by DEA agents which defendants challenge here.  That testimony concerned the operations of narcotics dealers and the characteristics of a narcotics "stash pad," and provided interpretation of the financial records seized from Diaz and the House.  In accordance with the precedents summarized above, the district court appropriately admitted this evidence.


59
C. Sufficiency of the Evidence.


60
All three defendants challenge the sufficiency of the evidence to support their convictions.  This court has repeatedly set forth the principles governing appellate sufficiency claims:


61
First, the defendant bears a "very heavy burden" in challenging the sufficiency of the evidence.  United States v. Buck, 804 F.2d 239, 242 (2d Cir.1986);  United States v. Grubczak, 793 F.2d 458, 462-63 (2d Cir.1986) (citations omitted).  The test is "whether the jury, drawing reasonable inferences from the evidence, may fairly and logically have concluded that the defendant was guilty beyond a reasonable doubt."    Grubczak, 793 F.2d at 463 (citations omitted).  In making such a determination, the evidence is viewed in the light most favorable to the government, and all permissible inferences are construed in its favor.  Grubczak, 793 F.2d at 463;  see United States v. Nersesian, 824 F.2d 1294, 1324 (2d Cir.), cert. denied --- U.S. ----, 108 S.Ct. 355, 98 L.Ed.2d 380 (1987).  If any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt, the conviction must be sustained.  United States v. Fiore, 821 F.2d 127, 128 (2d Cir.1987) (citing Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979);  United States v. Badalamenti, 794 F.2d 821, 828 (2d Cir.1986);  Grubczak, 793 F.2d at 462-63).    Nor is the government required to preclude every reasonable hypothesis which is consistent with innocence.  Fiore, 821 F.2d at 128.


62
United States v. Chang An-Lo, 851 F.2d 547, 553-54 (2d Cir.), cert. denied, --- U.S. ----, 109 S.Ct. 493, 102 L.Ed.2d 530 (1988).


63
The principles are equally settled with respect to the proof required to establish a conviction on a conspiracy charge:


64
Since "conspiracy by its very nature is a secretive operation," United States v. Provenzano, 615 F.2d 37, 45 (2d Cir.), cert. denied, 446 U.S. 953, 100 S.Ct. 2921, 64 L.Ed.2d 810 (1980), the elements of a conspiracy may be established through circumstantial evidence.  United States v. Soto, 716 F.2d 989, 991 (2d Cir.1983) (quoting United States v. Sanzo, 673 F.2d 64, 69 (2d Cir.), cert. denied, 459 U.S. 858, 103 S.Ct. 128, 74 L.Ed.2d 111 (1982)).  However, "absent evidence of purposeful behavior, mere presence at the scene of a crime, even when coupled with knowledge that a crime is being committed, is insufficient to establish membership in a conspiracy;  and mere association with conspirators is similarly insufficient."    United States v. Martino, 759 F.2d 998, 1002 (2d Cir.1985) (citations omitted);  United States v. Johnson, 513 F.2d 819, 823-24 (2d Cir.1975).  Thus, evidence of purposeful behavior designed to further a conspiracy must be shown to prove membership in that conspiracy.  See United States v. Torres, 519 F.2d 723, 726 (2d Cir.), cert. denied, 423 U.S. 1019, 96 S.Ct. 457, 46 L.Ed.2d 392 (1975);  Johnson, 513 F.2d at 823.


65
Chang An-Lo, 851 F.2d at 554.


66
We conclude that the evidence was sufficient to establish that all three defendants were knowing participants in a conspiracy to possess cocaine with intent to distribute it.  The evidence of the events prior to May 7, 1987, previously summarized, would establish at least a reasonable suspicion that the House was being used for narcotics activities, and the seizure of February 20, 1987 would give some indication, taken in connection with the later April events, that cocaine was involved.  Considering the events of May 7, 1987, all three defendants were clearly identified by Mansolillo and Torretta as being the three men they observed arriving at the House that morning.  Upon spotting the agents interviewing a neighbor, the three defendants continued driving on in an apparent attempt to deflect any suspicion or any connection with the House.  When they returned immediately thereafter, it was apparent to the agents that Riano was serving as a lookout as Perez entered the House, consistent with the defendants' earlier avoidance of the surveilling agents.  After Perez entered the house, he exited a short time later carrying the cardboard box which was ultimately found to contain $1,000,000 in cash.


67
Riano and Perez thereafter left the house and drove in a surveillance conscious manner to the Cue Variety Store, where others acted as lookouts while the two defendants remained inside the store for approximately an hour and a half.  The defendants then left behind the Chevrolet with $1,000,000 in its trunk, and departed in a different vehicle after jump starting it.  When apprehended, Riano had the latest Consolidated Edison bill for the House.  Finally, in addition to the $1,000,000 in cash seized from the Chevrolet, a Customs Receipt indicating that another $999,960 had been seized by Customs officials was found in the glove compartment of the Chevrolet.


68
Diaz, after arriving at the House with the other two defendants, eventually entered the House after Riano and Perez left, and emerged therefrom some time later carrying two large white plastic bags containing approximately $28,000 of currency in small denominations.  Diaz was also found to have approximately $30,000 on his person, as well as index cards with numerical notations.  DEA agent McCarthy, the government's expert witness, testified that those notes appeared to detail brokerage commissions on cocaine transactions.


69
Furthermore, even though no drugs were found on the persons of the defendants or at the House, Agent McCarthy testified that the red ledger found in the House appeared to list the dates of drug transactions, with the last transaction entry dated May 7, 1987, the day of the arrest, the names of the distributors, the amounts paid and amounts owing;  and that narcotics operations frequently used different locations, or "stash pads," to handle the money and narcotics involved in drug transactions.


70
Taken together, we deem this evidence adequate to establish a basis on which a rational trier of fact could have found the defendants guilty beyond a reasonable doubt, viewing the evidence in the light most favorable to the government and construing all inferences in its favor.  The suspicious activities of the defendants and their colleagues, the activities at the House inconsistent with normal residence and indicative of illegal activity, together with the large quantities of cash found on the person of Diaz and in the automobile abandoned by Riano and Perez, and the Customs Receipt in the vehicle's glove compartment evidencing a recent seizure of another $999,960, more than sufficed to link each of the defendants to an illegal conspiracy.  See United States v. Tramunti, 513 F.2d 1087, 1109 (2d Cir.)  (possession and removal from residence of $960,000 probative of illicit activity), cert. denied, 423 U.S. 832, 96 S.Ct. 54, 55, 46 L.Ed.2d 50 (1975);  see also United States v. Mabry, 809 F.2d 671, 687 (10th Cir.)  (large amount of unexplained cash probative of state of mind and intent in the context of a narcotics distribution scheme), cert. denied, --- U.S. ----, 108 S.Ct. 33, 98 L.Ed.2d 164 (1987);  United States v. Bernal, 719 F.2d 1475, 1478 (9th Cir.1983) (same).


71
The weakest link in the chain is the evidence of a cocaine conspiracy, but Agent McCarthy's testimony concerning the ledger seized at the House and the index cards seized from Perez, with perhaps some peripheral assistance from the seizure of February 20, 1987, provided an adequate basis for the jury's determination that the defendants were engaged in a conspiracy to possess cocaine with intent to distribute it.


72
D. Other Contentions.


73
We have considered the defendants' numerous other contentions, and find them to be without merit.

Conclusion

74
The judgments of conviction are affirmed.



*
 The Honorable Alan H. Nevas, United States District Judge for the District of Connecticut, sitting by designation


1
 A government witness testified that narcotics traffickers often use separate "stash pads" to deal with the drugs themselves and with the money related to those transactions


2
 Defendants challenge evidence concerning the events of February 20, 1987 as outside the scope of the charged conspiracy, which the indictment alleges to have commenced on March 1, 1987.  The indictment states, however, that the conspiracy commenced "on or about" March 1, 1987, and further describes that date as "approximate."    In any event, otherwise relevant evidence is not rendered inadmissible because it relates to events falling outside the time frame alleged in an indictment.  See United States v. Porter, 821 F.2d 968, 977-78 (4th Cir.1987), cert. denied, --- U.S. ----, 108 S.Ct. 1108, 99 L.Ed.2d 269 (1988);  United States v. Nemes, 555 F.2d 51, 52 (2d Cir.1977);  United States v. Grady, 544 F.2d 598, 604-05 (2d Cir.1976);  United States v. Bermudez, 526 F.2d 89, 95-96 (2d Cir.1975), cert. denied, 425 U.S. 970, 96 S.Ct. 2166, 48 L.Ed.2d 793 (1976);  United States v. Mallah, 503 F.2d 971, 981 (2d Cir.1974), cert. denied, 420 U.S. 995, 95 S.Ct. 1425, 43 L.Ed.2d 671 (1975)


3
 Fed.R.Evid. 103(d) authorizes us to "tak[e] notice of plain errors affecting substantial rights although they were not brought to the attention of the [trial] court."    See Houser, 804 F.2d at 570;  Rubin, 609 F.2d at 63-64.    Since, as indicated earlier, the applicability of Rule 404(b) here is questionable even if that rule had been properly invoked below, this case falls well short of calling for application of the "plain error" rule


