What is the test for admitting evidence that does not directly establish an element of the charge?

Independent of the matter of expert testimony, the trial court may admit evidence that does not directly establish an element of the offense charged, in order to provide background for the events alleged in the indictment. Background evidence may be admitted to show, for example, the circumstances surrounding the events or to furnish an explanation of the understanding or intent with which certain acts were performed. See United States v. Pedroza, 750 F.2d 187, 200 (2d Cir.1984). If the evidence admitted as background consists of, or repeats, out-of-court statements that are hearsay and are not admissible by virtue of an exception to the hearsay rule, the background evidence generally is not properly admitted for the truth of the matters there asserted. When, however, the background evidence is testimony of the witness based on his own knowledge, or is expert testimony as to opinions or inferences arrived at in reliance on the type of evidence normally relied on by experts in the field, it may properly be considered as evidence of the truth of the matters asserted.