Question: Suppose that the random variable X has a probability density function f x (x| theta) = exp (theta* w(x) -A(theta) + H(x)). (a) show that

Suppose that the random variable X has a probability density function

f_x(x| theta) = exp (theta* w(x) -A(theta) + H(x)). (a) show that the moment-generating function of Y (b) prove that Y is Normal.

(see the attached picture for complete question)

Suppose that the random variable X has a probability density functionfx(x| theta)

Suppose that the random variable X has a probability density function fx(ml9) = exp (ewe) Aw) + Hm (a) If Y = w(X) show that the momentgenerating function of Y is given by Mm) = Em = exp(A(6 + t) MD (b) Given in (a) that E9[Y] = (9 for 00

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