After a jury trial, the defendant was convicted of the crimes of arson in the third degree in vio*362lation of General Statutes § 53a-113 (a) and of using a motor vehicle without the owner’s permission in violation of General Statutes § 53a-119b (a) (1). On appeal, the defendant claims that the court erred in denying his motions for a mistrial due to (1) improper summation by the prosecutor, and (2) the trial court’s expression of its personal feelings before the jury. He further claims that it was error to admit evidence concerning the complainant’s state of mind.
The jury could reasonably have found the following facts. In the early morning of October 1, 1983, a fire was discovered in the back seat of a car parked in a lot on Mansfield Street, New Haven. The fire appeared to have been burning only a short time prior to its discovery. The car had no license plates, its left front tire was flat and there was fresh damage to the front bumper and hood. The automobile was registered in the name of Robert Gattison but was being used with his permission by his sister, Sherry Gattison, the live-in companion of the defendant. There were no signs of forced entry and it appeared that the car had been started with a key. The complainant, Sherry Gattison, had not given the defendant permission to drive the car. The defendant and the complainant were in the midst of breaking-up, and the defendant was planning to vacate the couple’s shared residence.
The complainant had parked her brother’s car in front of the couple’s apartment at 6 p.m. the prior evening, entered the apartment, and taken a nap. The defendant came home some two hours later, soon departed and returned at approximately 1:30 a.m. on October 1. At that time, the defendant told the complainant that he had taken the car and driven it into a tree and then had set the car afire and contemplated committing suicide in the flaming car. At approximately 3 a.m., the complainant received a telephone call from her mother who stated that the police found the vehicle in a park*363ing lot. The complainant then told the defendant she was going to telephone the police, but refrained from doing so because the defendant threatened her. The complainant did not, in fact, relay her knowledge of the original crime to the police until October 24,1983. The defendant’s car was similarly set on fire some twenty hours later. The defendant accused the complainant’s brother of setting the fire.
The defendant presented an alibi defense and alibi witnesses. The defendant’s alibi that he was with friends until returning to the apartment at 9:30 p.m. conflicted, however, with the alibi witnesses’ testimony that he was with them until 11:30 p.m.
The state’s chief witness was the complainant, Sherry Gattison. During the trial, she testified that she had not received any of the insurance proceeds from the car fire. The next day, the state’s attorney informed the court that the complainant had, in fact, received $1400 in insurance proceeds but had been confused by defense counsel’s questioning. The defense used this discrepancy to impeach the witness.
I
In his first claim of error the defendant asserts that his motion for a mistrial due to impermissible conduct by the prosecutor should have been granted. He claims that the prosecutor’s closing argument was improper in three ways. First, that she injected her personal ethics into the summation; second, that her mention of the fifth amendment presumption of innocence and reasonable doubt was an improper reference to the defendant’s failure to testify in his own behalf; and finally, that the prosecutor unfairly labeled him a “liar.”
“Article first, § 8 of the Connecticut constitution provides that ‘[n]o person shall be . . . deprived of . . . liberty . . . without due process of law . . . . ’ It is *364the prosecutor's duty to ensure that a defendant’s conviction comports with this provision. . . . ‘By reason of [her] office, [the prosecutor] usually exercises great influence upon jurors. [Her] conduct and language in the trial of cases in which human life or liberty are at stake should be forceful, but fair, because [she] represents the public interest, which demands no victim and asks no conviction through the aid of passion, prejudice, or resentment.’ ” State v. Couture, 194 Conn. 530, 564, 482 A.2d 300 (1984), cert. denied, 469 U.S. 1192, 105 S. Ct. 967, 83 L. Ed. 2d 971 (1985).
The role of a prosecutor is different from that of an ordinary advocate for the prosecutor’s duty is to see that justice is done. He or she must refrain from trying to arouse prejudice in the jury; State v. Falcone, 191 Conn. 12, 22, 463 A.2d 558 (1983); or from diverting their attention from their duty to base their conclusions on the evidence actually presented at trial. State v. Couture, supra, 562.
When a verdict is challenged on the basis of the prosecutor’s allegedly prejudicial remarks, the defendant bears the burden of proving the remarks prejudicial in light of the whole trial. “The fairness of the trial and not the culpability of the prosecutor is the standard for analyzing the constitutional due process claims of criminal defendants alleging prosecutorial misconduct.” State v. Binet, 192 Conn. 618, 628, 473 A.2d 1200 (1984).
The trial court is in a better position than we are to assess the arguments of counsel and is, therefore, granted wide discretion in determining their propriety. While the trial court’s actions are subject to review, we will reverse a decision only if the court clearly exceeded or abused its discretion resulting in obvious prejudice and injury to some party. State v. Evans, 165 Conn. 61, 65, 327 A.2d 576 (1973).
*365Although a prosecutor may, indeed should, argue to the jury all reasonable inferences from the evidence presented, an expression of his or her personal opinion of the credibility of a witness is not evidence and as such should not be argued to the trier of fact. Rules of Professional Conduct, Rule 3.4 (e) (formerly Code of Professional Responsibility, Canon 7, EC 7-24); accord 1 A.B.A. Standards for Criminal Justice (2d 1980) The Prosecution Function, § 3-5.8 (b). In this case, the defendant claims the prosecutor improperly “vouched” for the credibility of Sherry Gattison, by stating during rebuttal: “If you believe I’ve intentionally put on any perjured testimony in this case, if you believe, ladies and gentlemen of the jury, that I’ve lied to you, that I have misrepresented facts, then even though I’m not here as Mary Galvin — I am here as the prosecutor for the people of the State of Connecticut — for my ethics, I have to say to you if you believe that, acquit this man.”
While the prosecutor’s references to her personal ethics in this case were improper, “[w]e also recognize that ‘the limits of legitimate argument and fair comment cannot be determined precisely by rule and line, and something must be allowed for the zeal of counsel in the heat of argument.’ ” State v. Magnotti, 198 Conn. 209, 220, 502 A.2d 404 (1985). Defense counsel launched an ad hominem attack on the prosecutor in her own closing argument and accused the prosecutor of being unethical and disrespectful by calling Sherry Gattison as a witness when she knew she would commit perjury. In light of this, the assistant state’s attorney’s remark on rebuttal, while improper when viewed in isolation, was clearly invited by defense counsel and, as such, its prejudicial impact was not as great as if it had been unprovoked. State v. Falcone, supra, 23. We conclude, therefore, that while the prosecutor’s “voucher” of Sherry Gattison’s credibility was improper and may have been prejudicial in isolation, *366the defendant has not proved that it denied him the right to a fair trial. See State v. Glenn, 194 Conn. 483, 497, 481 A.2d 741 (1984).
In addition, the trial court admonished the jury that the comments of counsel were arguments, and not evidence. Defense counsel did not object or except to this charge or claim that it was inadequate to offset the prosecutor’s remarks. We conclude that the prosecutor’s remarks were not so prejudicial as to render the curative instruction ineffective. See State v. Couture, supra, 562.
The defendant also claims that the prosecutor’s reference to the fifth amendment presumption of innocence and its burden of proof beyond a reasonable doubt was improper. The relevant portions of the prosecutor’s closing argument are as follows: “The defense relies on the fifth amendment burden of proof beyond a reasonable doubt in their argument to you .... And, ladies and gentlemen, the fifth amendment burden of proof beyond a reasonable doubt is a protection for the innocent. As much as it is your responsibility to use and apply the fifth amendment burden of proof beyond a reasonable doubt standard to protect the innocent, it is your concomitant responsibility not to allow the fifth amendment burden of proof beyond a reasonable doubt to be a shield for the guilty. Ladies and gentlemen, your responsibilities are equal on both sides. The burden of proof beyond a reasonable doubt is a shield for the innocent. It is not a barrier to conviction for the guilty. . . . To find reasonable doubt in this case, you would have to speculate. You would have to surmise. You would have to engage in conjecture. And under the fifth amendment burden of proof beyond a reasonable doubt, you cannot speculate or surmise or guess . . . .” The defendant claims that such reference was an impermissible comment on his decision not to testify. Clearly a prosecutor may not comment at *367trial on a criminal defendant’s failure to testify. Griffin v. California, 380 U.S. 609, 615, 85 S. Ct. 1299, 14 L. Ed. 2d 106, reh. denied, 381 U.S. 957, 85 S. Ct. 1797, 14 L. Ed. 2d 730 (1965); State v. Cohane, 193 Conn. 474, 482, 479 A.2d 763, cert. denied, 469 U.S. 990, 105 S. Ct. 397, 83 L. Ed. 2d 331 (1984); State v. Allen, 9 Conn. App. 169, 178, 517 A.2d 1043 (1986). In a case involving alleged prosecutorial misconduct, if “the alleged misconduct involves the prosecutor’s indirect comment on the decision of the accused not to testify, the test is whether the comment was ‘ “of such character that the jury would naturally and necessarily take it to be a comment on the failure of the accused to testify.” ’ ” State v. Magnotti, supra, 216. This is not, however, the case before us. Here, the assistant state’s attorney’s mention of the fifth amendment was in reference to the state’s burden of proof beyond a reasonable doubt. The defendant is reading into these remarks something that is not there. He makes the broad, conclusory statement in his brief that “the jury sensibly and naturally would have understood the prosecution’s references to the fifth amendment” as a comment on his failure to testify. We disagree. The prosecutor’s remarks were an explanation that while the state must prove its case beyond a reasonable doubt it need not prove it absolutely. Such was the natural and necessary interpretation of the remarks. Thus, we conclude that the defendant has not demonstrated that the challenged comments were improper comments on his failure to testify.
The defendant’s final attack on the prosecutor’s summation revolves around the prosecutor’s use of the word “liar” to refer to the defendant. The prosecutor claimed that the defendant lied to police officers and a fire investigator prior to trial. The record in this case establishes that the defendant’s statements to the police prior to trial conflicted with the evidence presented at *368trial by the police and even the defendant’s alibi witnesses. While we agree that a prosecutor should not attempt to inflame the passions or prejudices of the jury to divert their attention from their duty to decide the case on the evidence alone, this does not mean that the prosecutor cannot present a strong and cogent argument. State v. Carr, 172 Conn. 458, 470, 374 A.2d 1107 (1977); State v. Allen, supra, 178, 181. A prosecutor may not comment on facts not in evidence. State v. Ferrone, 96 Conn. 160, 169, 113 A. 452 (1921); see also State v. Glenn, supra, 492-93. In this case, however, the inconsistencies to which the prosecutor referred were in evidence through witnesses other than the defendant who exercised his right not to testify. Our review of the record makes clear that the prosecutor was referring to testimony of alibi witnesses presented by the defendant which conflicted with pretrial statements made by the defendant which were admitted into evidence. Thus, the prosecutor’s remarks referred to facts in evidence and on the record and were an attempt to highlight the serious flaws in the defendant’s case.
We do not condone the challenged portions of the prosecutor’s arguments in this case or her use of the word “liar.” Yet we are convinced, given the context of the trial as a whole, including particularly the impassioned and improper comments of defense counsel and her use of the word “liar,” that the prosecutor’s comments did not deny the defendant a fair trial.
II
The defendant’s second claim of error is that he was entitled to a mistrial since the court expressed its personal feelings before the jury by interfering with the defendant’s right to cross-examine certain of the state’s witnesses. It is indisputable that the defendant is entitled to fully confront and cross-examine the witnesses appearing against him. U. S. Const., amend. VI, *369XIV; Conn. Const., art. 1, § 8; see also State v. Hackett, 182 Conn. 511, 517, 438 A.2d 726 (1980).
The defendant claims that the court improperly interfered when it prohibited the use of the words “lying” and “perjury” when the state’s chief witness, Sherry Gattison, was being cross-examined. The court stated; “I think it’s sufficient to say that she says she was confused. Whether that’s to be believed or not, it’s within the jury’s function; and based on that confusion, she did not tell the truth yesterday.” The defendant argues that this comment exposed the jury to the judge’s personal opinion of the witness’ credibility. We recognize that a trial judge plays an important and authoritative role in any court proceeding. While the judge must be impartial, he may intervene in an attempt to reach the truth when counsel has failed to do so. A judge should not assume the role of an advocate and must refrain from making comments which favor or condemn any party before the jury. A fine line separates proper and improper judicial conduct and the judge must strive to appear impartial and detached. See State v. Fernandez, 198 Conn. 1, 11, 17, 501 A.2d 1195 (1985); see also State v. Camerone, 8 Conn. App. 317, 325, 513 A.2d 718 (1986). Nevertheless, we recognize that a trial judge has the right to question a witness when necessary to eliminate confusion in a question or an answer or to restrain a rambunctious witness. State v. Smith, 200 Conn. 544, 549, 512 A.2d 884 (1986). In this case, the trial court did not otherwise restrict the extensive cross-examination by the defendant. It did not indicate its belief or disbelief in Sherry Gattison’s testimony, since it specifically instructed the jurors that it was up to them to judge her credibility. Hence, the trial court’s comments did not deprive the defendant of his right to a fair trial or to an impartial jury.
Ill
Finally, the defendant claims that the trial court erred in allowing Sherry Gattison to testify that her *370belief that her brother’s car was equipped with an anti-theft device, which precluded its use without a key, was based solely on the fact that her brother told her it was so equipped. The court allowed the testimony under the “state of mind” exception to the hearsay rule. The witness explained that she delayed reporting the defendant’s involvement in the car fire because she was afraid she would be blamed for the fire since the car had an anti-theft device and she alone possessed the keys. The defendant argues that the brother’s out-of-court statement to the witness regarding the anti-theft device is inadmissible hearsay. “It is an elementary premise of evidentiary law, however, that testimony is considered to be hearsay only when it is an out-of-court statement 'offered to establish the truth of the matters contained therein.’ ” State v. Delgado, 8 Conn. App. 273, 282, 513 A.2d 701 (1986); State v. Sharpe, 195 Conn. 651, 661, 491 A.2d 345 (1985). If such a statement is offered, instead, to show the defendant’s state of mind upon hearing it, it is not offered for its truth. See C. McCormick, Evidence (3d Ed. 1984) § 249, p. 734. In the present case, the brother’s out-of-court statement was not offered to prove whether the car was, in fact, equipped with an anti-theft device. It was offered to show only that the witness thought it was so equipped. Thus, it was not hearsay. Since the testimony sought to be introduced here was not hearsay and was not irrelevant or collateral to an issue in the case it was properly admitted. State v. Delgado, supra, 282.
There is no error.
In this opinion Hull, J., concurred.