Normal random variables (2nd)

Proggy99

1. Homework Statement
Let X be a standard normal random variable. Calculate E(XcosX), E(sinX), and $$E\left(\frac{X}{1+X^{2}}\right)$$

2. Homework Equations

3. The Attempt at a Solution
I have no idea where to start with this. I am not seeing any connection between it and the chapter reading/examples. Can someone show me how to start on one of them. Thanks.

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e(ho0n3

Why not start by writing down what E(X cos X) means from the definition of expected value.

Proggy99

Why not start by writing down what E(X cos X) means from the definition of expected value.
Well, I know that the expected value is the mean, or average, of the possible answers. I also know that xcosx creates a graph that is symmetrically when turned at a 180 degree angle around 0. This tells me that there are positive and negative values that offset each other leaving the answer to be 0. I know that sinx does the same thing, with offsetting values leaving the average of 0. I know that the third equation does the same thing, where 1 offsets -1, 2 offsets -2, and so forth, again leaving 0. So know the expected value of all three equations is 0 from an ability to reason that it is so. But I am not sure how to go about calculating the values as the problem wants me to do.

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