Problem: Suppose we repeatedly and independently pick a random n-bit integer until we find one that is prime. Let X be the number of times we have to sample before successfully finding a prime (assume we do prime-checking in a deterministic way). (a) What kind of random variable is X? 1 (b) Find an upper bound on E[X]. (c) Find an upper bound on P[X > m]. Find a function m(n) that makes this upper bound a negligible function of n.