Chapter 24, PROBLEM SET 24.5 #11

Find the probability that none of three bulbs in a traffic signal will have to be replaced during the first 1500 hours of operation if the lifetime X of a bulb is a random variable with the density f(x) = 6[0.25 - (x - 1.5)^{2}] when 1 ≤ x ≤ 2 and f(x) = 0 otherwise, where x is measured in multiples of 1000 hours.

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