.. Cast a die a number of independent times until a six appears on the up side of the die. (a) Find the pmf p(x) of X, the number of casts needed to obtain that first six. (b) Show that p(x) = 1. =1 (c) Determine P(X = 1, 3, 5, 7, ...). (d) Find the cdf F(x) = P(X x).