Question: P(X = k) = (1 )k1 for k = 1, 2, . . . , where satisfies 0 < < 1. A

P(X = k) = (1 − α)αk−1 for k = 1, 2, . . . , where α satisfies 0 < α < 1. A new light bulb is inserted in its socket on day 0. Show that the probability that the bulb has to be changed on day n is 1 − α, independently of n.

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