# Question: Expand the moment generating function of the gamma distribution as a

Expand the moment–generating function of the gamma distribution as a binomial series, and read off the values of µ'1, µ'2, µ'3, and µ'4.

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Use the results of Exercise 6.13 to find α3 and α4 for the gamma distribution. A random variable X has a Pareto distribution if and only if its probability density is given by Where α > 0. Show that µ'r exists only if r < α. If a random variable X has a uniform density with the parameters a and β, find its distribution function. Use the Maclaurin’s series expansion of the moment-generating function of the standard normal distribution to show that (a) µr = 0 when r is odd; (b) µr = r! 2r / 2r/2(r/2)! when r is even. If X and Y have a bivariate normal distribution and U = X + Y and V = X – Y, Find an expression for the correlation coefficient of U and V.Post your question