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Practice Problem: Recover the probability mass function from the characteristic function
A discrete random variables X has a moment generating (characteristic) function $ M_X(s) $ such that
$ \ M_X(j\omega)= 3+\cos(3\omega)+ 5\sin(2\omega). $
Find the probability mass function (PMF) of X.
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Answer 1
I tried taking the inverse fourier transform since PX(x) = F^-1 { Mx(jw)}, however my resultant pmf has j (sqrt(-1)) in the answer, and doesn't sum to 1...
Are we finding an invalid pmf or am i approaching the problem wrong?
-AW
Answer 2
Write it here.
Answer 3
Write it here.
