19. Sum of biased dice. Let S be the sum of numbers obtained by rolling two biased dice with possibly different biases described by probabilities p1, . . ., p6, and r1, . . ., 6, all assumed to be nonzero. a) Find formulae for P(S = k ) for k = 2, 7, and 12. b) Show that P(S = 7) > P(S = 2)- + P(S = 12)- T15. Question 5 Let X be a (continuous) uniform random variable on the interval [0, 1] and Y be an exponential random variable with parameter A. Let X and Y be independent. What is the PDF of Z = X +Y