Find the expected number of ?ips

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1. Let Xi , i ?: 1, be independent random variables with pj = P{X = j}, j ?: 1. If pj = j/10, j = 1, 2, 3, 4, ?nd the expected time and the variance of the number of variables that need be observed until the pattern 1, 2, 3, 1, 2 occurs.

2. A coin that comes up heads with probability 0.6 is continually ?ipped. Find the expected number of ?ips until either the sequence thht or the sequence ttt occurs, and ?nd the probability that ttt occurs ?rst.

Reference no: EM131005877

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