The mgf of a random variable X has the following form: e-8t et 5 Mx(t) =...

Question

Question

The mgf of a random variable X has the following form: e-8t et 5 Mx(t) = 0.64 . Find ElYX). Answer:-0.2

math Statistics-And-Probability

Answer 1

Answer #1

as we know that mgf of a discrete varible M_x(t) = $\sum$ P(x=x)*e^tx

comparing it with given MGF:

P(X=0) =0.6

P(X=-8) =1/5 =0.2

P(X=1) =1/5 =0.2

hence E( $\sqrt[3]{X}$ ) = $\sum$ xP(x) =(-8)^1/3*0.2+0^1/3*0.6+(1)^1/3*0.2 =-0.4+0.2 =-0.2

Answer 2

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