Normal random variables (2nd)

[Proggy99]

Homework Statement

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

Homework Equations

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.

 

[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.