Question 9: We have a random experiment with space of elementary events = {a,b,c,d,e,f}. We take = 20 and P(A) = |A for any A E. We consider X: R a map defined by the following relation: a) Prove that X is a random variable on [n,A,P]? b) Calculate the probability P(X 4.75)? -2 X(w) = 0 5 c) Determine the distribution function F(z) for all x ER. d) Calculate E(X2) of this random variable. -4- for a= a,b for w=c for @= d,e,f