Assume that the time in hours until the failure of a transis

Assume that the time in hours until the failure of a transistor is exponentially distributed with a mean of 100.

a.Find the probability that the transistor will fail in less than 15 hours.

b.What is the variance of this exponential distribution?

Solution

a)

Here,

P(X<x) = 1 - exp(-x/100)

Thus,

P(x<15) = 1 - exp(-15/100) = 0.139292024 [ANSWER]

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B)

For an exponential distribution.

variance = (mean)^2 = 100^2 = 10000 [ANSWER]