Question

Question 18:

a) Compute the moment generating function, MGF, of a normal random variable X with mean µ and standard deviation σ.

b) Use your MGF from part a) to find the mean and variance of X.

Answer 1

thank you please thumb up

Solution XN N14102/ w fox) = furen e f (x-4)2 -20<x<* M.G' F of Nosimal Distribution Mxt = Dabafos de har et opl-02-41840) sebre ex P{ $(1402)} cxp(-7812) 47 (: 45X4) servit *P4 (z? &#02) 3dz e ser exp[={{{ z- ost)2 – on?t?)] dz put to L x Bord exp{{ (z_6+1}.dz = putt effe º expl-1*e) down Mlt) = elit to the Hence 6 use MGF Part 6 kxCtl = loge MX(t) = loge (elut + oth) = uttt az Mean= ki = Coefficent of t kylt1 = 1 الد= Mean | variance =k2 = Coefficent of Binky CH Fo? variance =02