Nick and penny are independently performing independent bernoulli trials. for concreteness, assume that nick is ipping a nickel with probability p1 of heads and penny is ipping a penny with probability p2 of heads. let x1; x2; : : : be nick's results and y1; y2; : : : be penny's results, with xi bern(p1) and yj bern(p2). (a) find the distribution and expected value of the rst time at which they are simultaneously successful, i. e., the smallest n such that xn = yn = 1. hint: de ne a new sequence of bernoulli trials and use the story of the geometric. (b) find the expected time until at least one has a success (including the success). hint: de ne a new sequence of bernoulli trials and use the story of the geometric