Lawrence Lewis, Jr., was tried and convicted under 18 U.S.C. § 1111 (1982) for the second-degree murder of his two-year-old stepson, Jordan Francis..

On appeal, the defendant challenges: 1) the prosecutor’s use of a peremptory challenge to excuse a black juror; 2) the trial court’s exclusion of expert psychiatric testimony concerning the defendant’s state of mind; and 3) the trial court’s admission of evidence concerning a prior battery of the same child by the defendant.

On the evening of June 17, 1986, the defendant brought his unconscious stepson to the hospital emergency room at the Fort Huachuca Army base in Arizona. Attempts to revive the child were unsuccessful. Examinations by an Army doctor and an Army criminal investigator revealed recent bruises to the child’s thigh, arm, back and forehead. An autopsy indicated that the child died from severe brain swelling as a result of blunt force injuries to his head and body.

At trial, the defendant testified that in disciplining the child for defecating on the floor he had hit him with a belt and slapped him on his head before giving him a bath, which the defendant viewed as punishment. He testified that as a child he had been subjected to severe corporal punishment and that he believed such techniques were necessary to discipline children. Because the defendant conceded that he had killed the child, the only issue at trial was whether he possessed the “malice aforethought” that is an element of second-degree murder under 18 U.S.C. § 1111 (a) (1982).

I. Jury Selection

The defendant, who is black, argues that he was deprived of his right to fair representation on his jury panel because the prosecutor exercised a peremptory challenge to remove a black member of the jury panel from the defendant’s panel. The prosecutor exercised her nine peremptory strikes to excuse eight white veniremen and one of the two black veniremen sitting on the 36-juror panel. The remaining black member of the panel sat on the jury.

The defendant argues that the peremptory challenge against the black venireman is reversible error under Batson v. Kentucky, 476 U.S. 79 , 106 S.Ct. 1712 , 90 L.Ed.2d 69 (1986). Batson held that the equal protection clause “forbids the prosecutor to challenge potential jurors solely on account of their race or on the assumption that black jurors as a group will be unable impartially to consider the State’s case against a black defendant.” Id. 106 S.Ct. at 1719 .

Under Batson , “a black defendant alleging that members of his race have been impermissibly excluded from the venire may make out a prima facie case of purposeful discrimination by showing that the totality of relevant facts gives rise to an inference of discriminatory purpose.” Id. at 1721; see United States v. Thompson, 827 F.2d 1254, 1256-57 (9th Cir.1987). Only after the defendant has established a prima facie case is the prosecutor required to rebut the inference of discrimination by presenting a neutral basis for her challenges. See Batson, 106 S.Ct. at 1721 ; Thompson, 827 F.2d at 1256-57 .

Batson sets forth what is essentially a two-part inquiry for determining whether a defendant has established a prima facie case of discriminatory exclusion by the prosecutor. Batson, 106 S.Ct. at 1722-23 . First, the defendant “must show that he is a member of a cognizable racial group, ... and that the prosecutor has exercised peremptory challenges to remove from the venire members of the defendant’s race.” Id. at 1723. Then, the defendant must show circumstances that “raise an inference that the prosecutor used [peremptory challenges] to exclude the veniremen from the petit jury on account of their race.” Id.

The defendant has satisfied the first requirement of the prima facie inquiry, but the record does not demonstrate circumstances raising an inference of prosecutorial bias. The defense counsel made no showing beyond the fact of the exercise of a peremptory strike against a black venire.man. There was no suggestion that the questions or statements on voir dire showed bias or that the prosecutor evidenced a “pattern” of such strikes in the particular venire, nor did the defense call any other circumstances to the court’s attention. See Batson, 106 S.Ct. at 1723 ; see also United States v. Vaccaro, 816 F.2d 443, 457 (9th Cir.) (finding that the systematic exclusion of blacks could not be inferred from the exclusion of the only two black veniremen), cert. denied, — U.S. -, 108 S.Ct. 262 , 98 L.Ed.2d 220 (1987).

Without expressly ruling on whether a prima facie showing had been made, the trial judge observed that the peremptory strike might implicate Batson . The prosecutor then proceeded to place her justifications on the record. The defendant argues that these justifications were “shams” and that they raise an inference of discriminatory intent sufficient to establish a prima facie case.

For the purposes of this appeal, we accept the defendant’s argument that the prosecutor’s volunteered justifications may be considered as part of his prima facie case. See Batson, 106 S.Ct. at 1721 (holding that a prima facie case may be shown by “the totality of relevant facts”). We assume that the prosecutor’s justifications will not establish a prima facie case if they are adequate to rebut an inference of discriminatory intent.

Because the trial court’s findings concerning discriminatory intent rest largely upon evaluation of credibility, such findings are entitled to “great deference.” Batson, 106 S.Ct. at 1724 n. 21. Under this standard, the trial court’s finding that the prosecutor rebutted any inference of discriminatory intent is not clearly erroneous. The venireman’s age and lack of family may have appeared relevant to the prosecutor in a case involving child abuse and reasonably could be deemed to constitute a non-discriminatory basis for striking the venireman. See Batson, 106 S.Ct. at 1723 (“emphasizing] that the prosecutor’s explanation [to rebut an inference of discrimination] need not rise to the level justifying exercise of a challenge for cause”). We therefore find no reversible error in the peremptory challenge.

II. Expert Testimony

The defendant challenges the district court’s exclusion of expert psychiatric testimony relating to his state of mind. The offer of evidence was tendered on the day of trial, contrary to the rule requiring timely advance notice of intent to use such expert testimony. The defendant sought to introduce expert testimony from a psychiatrist who had examined the defendant and would have testified concerning his mental state and motivation.

The district court’s decision concerning the exclusion of evidence is reviewed for an abuse of discretion or for manifest error. See United States v. Binder, 769 F.2d 595, 601-02 (9th Cir.1985). This testimony was properly excluded under Fed.R.Evid. 704, which prohibits expert testimony “as to whether the defendant did or did not have the mental state or condition constituting an element of the crime charged or of a defense thereto. Such ultimate issues are matters for the trier of fact alone.” Fed.R.Evid. 704.

The defendant has failed to establish that the psychiatrist’s testimony would have concerned a topic requiring expert testimony but would not have gone to the defendant’s state of mind. If the psychiatrist’s testimony was intended to support the defendant’s assertions that he lacked parenting skills and was unaware of the proper means of disciplining children, expert testimony was inappropriate. See Fed.R.Evid. 702 (allowing expert testimony only where “specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue”). Furthermore, the district court had the discretion to exclude such testimony as unnecessarily duplicative of prior testimony by the defendant and other witnesses. See Fed.R.Evid. 403 (providing that relevant evidence may be excluded “if its probative value is substantially outweighed by ... considerations of undue delay, waste of time, or needless presentation of cumulative evidence”).

The district court did not abuse its discretion in excluding the psychiatrist’s testimony.

III. Prior Bad Acts

The defendant challenges the district court’s decision to admit the testimony of two maintenance workers that they saw the defendant severely punish his stepson six weeks before the child’s death. The two workers testified that the defendant had repeatedly hit his stepson on the head and face because the child was unable to put his shoes on. They also testified that they saw the defendant carrying the child to the bedroom while holding a belt in his hand.

The district court ruled pretrial that this prior incident was admissible, stating:

We review the district court’s decision to admit evidence of a prior bad act under Fed.R.Evid. 404(b) for an abuse of discre tion. See United States v. Feldman, 788 F.2d 544, 557 (9th Cir.1986), cert. denied, — U.S. -, 107 S.Ct. 955 , 93 L.Ed.2d 1003 (1987). “Relevant evidence of crimes not charged in the indictment is admissible under Fed.R.Evid. 404(b) unless its only relevance is to show criminal disposition.” United States v. Unruh, 827 F.2d 501, 516 (9th Cir.1987). However, evidence admissible under Fed.R.Evid. 404(b) must be excluded unless its probative value outweighs its prejudicial effect, as required by Fed.R.Evid. 403. United States v. Bradshaw, 690 F.2d 704, 709 (9th Cir.1982), cert. denied, 463 U.S. 1210 , 103 S.Ct. 3543 , 77 L.Ed.2d 1392 (1983).

Under Fed.R.Evid. 404(b), evidence of prior acts is admissible to prove intent when “the prior act is similar and close enough in time to be relevant” and “the evidence of the prior act is clear and convincing.” United States v. Hooton, 662 F.2d 628, 635 (9th Cir.1981), cert. denied, 455 U.S. 1004 , 102 S.Ct. 1640 , 71 L.Ed.2d 873 (1982). The testimony concerning the prior act was relevant because the prior act occurred only six weeks before the child’s death and because it involved the defendant’s abuse of the child; as the trial court observed, the prior act tended to demonstrate his intent. Evidence of the prior act was clear and convincing, given that two witnesses testified in court — and the defendant admitted — that he had beaten his stepson on that date.

The defendant argues that the testimony should have been excluded under Fed.R. Evid. 403, which allows exclusion where the evidence’s “probative value is substantially outweighed by the danger of unfair prejudice.”

Evidence of the prior incident had probative value in disproving claims that the defendant lacked intent or that the child died by accident. See Hooton, 662 F.2d at 634-35 (admitting evidence of a prior act where lack of intent will be raised as a defense); see also United States v. Woods, 484 F.2d 127, 133-34 (4th Cir.) (finding that prior injuries to a child were relevant in proving the defendant’s intent and the absence of accident), cert. denied, 415 U.S. 979 , 94 S.Ct. 1566 , 39 L.Ed.2d 875 (1974); United States v. Harris, 661 F.2d 138 (10th Cir.1981) (same). Additionally, the testimony was probative because 18 U.S.C. § 1111 (a) (1982) requires the government to prove that the defendant acted with “malice aforethought.” See United States v. Celestine, 510 F.2d 457, 459 (9th Cir.1975) (holding that malice aforethought “may be inferred from circumstances which show ‘a wanton and depraved spirit, a mind bent on evil mischief without regard to its consequences’ ”) (quoting Government of Virgin Islands v. Lake, 362 F.2d 770, 774 (3rd Cir.1966)).

The evidence was not overly prejudicial because the defendant already had admitted beating the child at the time of his death and on other occasions. Given his admission, we must reject the defendant’s claim that the evidence was highly prejudicial because “a jury is likely to infer that, having once committed a crime, the defendant is likely to do it again.” See United States v. Bejar-Matrecios, 618 F.2d 81, 84 (9th Cir.1980).

The trial court did not abuse its discretion in admitting evidence of the defendant’s prior act. The court properly instructed the jury that the prior bad act did not imply that the defendant had a criminal propensity. We therefore find no reversible error.

CONCLUSION

The prosecutor did not violate the defendant’s right to equal protection by exercising a peremptory challenge against a black venireman. The trial court did not err by excluding the psychiatrist’s testimony or by admitting testimony concerning the defendant’s prior bad act. The conviction of the defendant is AFFIRMED.

. Section 1111(b) makes a federal offense of any murder committed "[w]ithin the special ... territorial jurisdiction of the United States." 18 U.S.C. § 1111 (b) (1982). . Although the holding in Batson was based upon the equal protection clause of the fourteenth amendment, it is applicable to federal court convictions under the equal protection component of the fifth amendment due process clause. See, e.g., Bolling v. Sharpe, 347 U.S. 497, 499 , 74 S.Ct. 693, 694 , 98 L.Ed. 884 (1954); United States v. Avendano-Camacho, 786 F.2d 1392, 1394 (9th Cir.1986). . The Batson court stated the prima facie inquiry in terms of a three-part test, but the second factor stated constitutes a conclusive presumption rather than a distinct factual inquiry: "[T]he defendant is entitled to rely on the fact, as to which there can be no dispute, that peremptory challenges constitute a jury selection practice that permits ‘those to discriminate who are of a mind to discriminate.’” Batson, 106 S.Ct. at 1723 (quoting Avery v. Georgia, 345 U.S. 559, 562 , 73 S.Ct. 891, 892 , 97 L.Ed. 1244 (1953)). See Thompson, 827 F.2d at 1256-57 (interpreting the prima facie inquiry to require two showings). . The prosecutor stated: As to Mr. Tatum, I struck him because the jury service indicated that he had no children. Therefore, he wasn’t involved in a family life. Also he’s from the state of Texas, and has lived there for many years. And I felt that perhaps, given that kind of background, and his older age, that he may himself have been subjected to some kind of harsh discipline. .The defendant claims that discriminatory intent is demonstrated because the prosecutor failed to strike other veniremen possessing some of the same characteristics that she cited as justifications for striking the black venireman. We recognize, however, that the decision whether to strike a venireman hinges upon the interplay of various factors and that no unchallenged juror possessed all the cited characteristics. . The cases cited by the defendant for the proposition that expert testimony is admissible when the jury must assess the defendant’s state of mind are inapplicable here because those cases involved claims of insanity or brain damage, matters on which expert testimony is appropriate. See United States v. McBride, 786 F.2d 45 (2d Cir.1986); Boykins v. Wainwright, 737 F.2d 1539 (11th Cir.1984), cert. denied, 470 U.S. 1059 , 105 S.Ct. 1775 , 84 L.Ed.2d 834 (1985); United States v. Frisbee, 623 F.Supp. 1217, 1223 (N.D.Cal.1985). . The government also argues that exclusion of the expert testimony was proper because the defendant violated Fed.R.Crim.P. 12.2(b) by failing to give the. prosecution timely notice of his intent to employ psychiatric testimony. The district court expressly stated that it did not exclude the testimony on this ground, although it cited no "cause” for allowing the late filing. See Fed.R.Crim.P. 12.2(b). Because we find the evidentiary issues dispositive, we decline to reach the notice issue. . The defendant also argues that the government could not introduce evidence of prior bad acts in its case in chief because "[i]t is an accepted principle that only after the defense has presented its case can the trial judge know if intent or knowledge or any other element constituting an exception to the exclusion rule is truly a disputed issue in the case.” Hooton holds that "even in general intent crimes, the government can offer evidence of other acts as part of its case-in-chief when it is obvious that the defense will raise lack of intent as a defense.” Hooton, 662 F.2d at 635 . Because the defendant had admitted that he committed the act, it was obvious that lack of intent would be raised as a defense.