Question: Prove, using the Gaussian density pX(x) = 1 22 e(x)2/2 that the mean value of r.v. X is indeed , i.e. compute the integral EX

Prove, using the Gaussian density pX(x) = 1 22 e(x)2/2 that the mean value of r.v. X is indeed , i.e. compute the integral EX Z xpX(x)dx = . . . = . (show by direct calculation that it equals .). Hint: this problem is trivial, it suffices to use a well known result for Gaussian integrals

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