The lifetime, in weeks, of a certain type of transistor is known to follow a gamma distribution with mean 10 weeks and standard deviation √50 weeks. (a) What is the probability that a transistor of this type will last at most 50 weeks?

(b) What is the probability that a transistor of this type will not survive the first 10 weeks?

Gamma with parameters (a,b) has mean a.b and variance a.b^2 a.b = 10 a.b^2 = 50 variance / mean = b = 50/10 = 5. Hence a = 2. P(X<10) = 1/25 . integral from 0 to 10 ( x . exp(-x/5)) dx Let u = x/5 du = 1/5 dx P(X<10) = P( U < 2) = integral from 0 to 2 ( u . exp(-u)) du Then do integration by parts to evaluate. You should get 0.59399

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