8. Find the moment generation function of a random variable X that follows the uniform distribution between 5 and 7;f(x) = 1/2, for 5 S x S 7. 9. Find the moment generating function for the random variable Z = 2X + 4Y, where X and Y are independent Gamma variables with (shape a: 2 , rate A: 2) and (shape a: 2, rate A: 4 respectively. What is the distribution of Z? 10. (a). Suppose the Taylor expansion of the moment generating function of a random variable is m(t) = 1 + 3t + 6t2 + . Find the mean and variance of this random variable. (b). Please examine the Taylor expansion of the following three functions and tell which ones cannot be moment generating functions : m1(t) = 0.5 + t + 2:2 + m2(t) = 1 +3: +312+ m3(t)=1 Zr + 31:2 +