Throw a coin until a head turns up for the second time, where p is the probability of a throw results in heads and we assume that the outcome of each throw is independent to the previous outcomes. Let X be the number of times we have thrown the coin. a.
Determine P(X = 2), P(X = 3), and P(X = 4). b. Show that P(X = n) = (n − 1)p2(1 − p)n−2 for n ≥ 2.
Determine P(X = 2), P(X = 3), and P(X = 4). b. Show that P(X = n) = (n − 1)p2(1 − p)n−2 for n ≥ 2.
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