Question

A moment-generating function of X is given by M(t) = 0.3et +0.4e2t +0.2e3t +0.1e5t.(e) Find the mgf of X2 – 1.

An exact same question has been posted several times here before, but without this part (e). So, would you please provide a complete solution and answer for part (e)? Thank you.

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Answer #1

(e) X has values 1,2,3,5 with probabilities 0.3, 0.4, 0.2, 0.1 respectively.

Then X2-1 has values 0,3,8,24 with probabilities 0.3, 0.4, 0.2, 0.1 respectively.

Thus the MGF of X2-1 is,

M(t) = 0.3+0.4e3t+0.2e8t+0.4e24t​​​​​​​

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