variance of = E{(X - ux)'}, skewness E{(X - ux)3}/ox and excess kurtosis E{(X - ux)* }/ox - 3. 3. Let X be a normal random variable with mean , variance o', pdf f(x) = and mof M (t) = cut+10212 (a) Prove, by identifying the moment generating function of a +bX, that a+bX ~ N(a + bu, b202). (b) Prove, by identifying the pdf of a + bX (via the cdf), that a + bX ~ N(a + bu, 6202 ) . 4. Let A random variable X is lognormal if Y = In X, the natural logarithm of X, is ally distributed