5. Let the continuous random variable ) have the following probability density function: p(x) = aBx*-1e-Bx" for x > 0 (and p(x) = 0 otherwise) where a and B are positive parameters. (a) If a = 1, what is the name of this probability distribution? (b) Use the definition of the expected value to show that: E(X) = 8-1/@ . [(1 + 1/a) where I(.) is the gamma function (Hint: use the substitution u = Bx*). (c) If a = 1/4 and B = 2, use part (b) to find the expected value of X