- #1

RoshanBBQ

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## Homework Statement

Find the expected value of cos(A+B) where A is a constant and B is a random variable with a pdf f(b). Present the answer in terms of f(b).

## The Attempt at a Solution

I don't know how far I can go with the answer -- I have tried for a bit now to remove an integral with no success.

[tex]\int\limits_{-\infty}^{\infty}\cos(A+b)f(b)\, db[/tex]

From here, I tried integration by parts, which ended in evaluating a cosine at infinity (for the uv term). I thought perhaps to find the pdf of the r.v. C = cos(A + B) and then integrate cf_c(c), but the issue of removing the integral seems strong as ever with that approach too.

Do you think the teacher intends for the answer to have an integral in it?