1 Let xi X be a random sample from a distribution with the L

1. Let (xi.... X.) be a random sample from a distribution with the Let(X, function (pdf) given by 1. , Xn) be a ran doin sample from a distribution with the probability density where-oo

Solution

Find the MGF for the give f(x)

MGF = E(e^tx) =

Integrating and expanding we get

MGF = 1+ (beta+gamma) t + beta^2+(beta+gamma)^2 t^2+/......

Hence E(X) = coefficient of t in expanson of MGF

=  (beta+gamma)

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E(x²) =  coefficient of t²=

beta^2+(beta+gamma)^2