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Q45Section C (Section C)45 of 60

Expected runs in Bernoulli trials

Consider a sequence of independent Bernoulli trials, where 34\frac{3}{4} is the probability of success in each trial. Let XX be a random variable defined as follows: If the first trial is a success, then XX counts the number of failures before the next success. If the first trial is a failure, then XX counts the number of successes before the next failure. Then 2E(X)2E(X) equals __________

Numerical answer: type the number (no options).

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