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Normal random variables (2nd)

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Let X be a standard normal random variable. Calculate E(XcosX), E(sinX), and [tex]E\left(\frac{X}{1+X^{2}}\right)[/tex]


    2. Relevant 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.
     
  2. jcsd
  3. Mar 29, 2009 #2
    Why not start by writing down what E(X cos X) means from the definition of expected value.
     
  4. Mar 30, 2009 #3
    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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