Bernoulli Distribution: Definition and Examples
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Bernoulli Distribution: Definition and Examples
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(a) Independent Bernoulli trials are performed, with probabilit... | Filo
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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 Be
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