Solution-Find probability that the first successes are

Find probability that the first successes are simultaneous

Reference no: EM131812348

Question: Nick and Penny are independently performing independent Bernoulli trials. For concreteness, assume that Nick is flipping a nickel with probability p1 of Heads and Penny is flipping 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 first time at which they are simultaneously successful, i.e., the smallest n such that Xn = Yn = 1. Hint: Define 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: Define a new sequence of Bernoulli trials and use the story of the Geometric.

(c) For p1 = p2, find the probability that their first successes are simultaneous, and use this to find the probability that Nick's first success precedes Penny's.

Reference no: EM131812348

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Find probability that the first successes are simultaneous

Reference no: EM131812348

Reference no: EM131812348

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