fast rate speed

2. (20 points) Let p E (0, 1) and let X and Y be independent Geometric(p) random variables. Recall that the probability mass function for a geo- metric random variable is P(X = k) = p(1 - p)*- for k e {1, 2, 3, 4, 5, ...}. (a) For every positive integer k E N calculate P(X