Question

For a particular machine, its useful lifetime (random variable T) is modeled by an exponential probability density function. Given that the expected lifetime of this machine is 10 years, find the exponential probability density function f(t) for random variable T

Answer 1

We are given that T~Exponential(λ) for some λ.

Thus, the probability density function of T is given by:

Moreover, the expected value of T is given by:

But, in question, we are given that the expected value of T (expected lifetime of machine) is 10 years.

=> E(T) = 10 .................(2)

From equations (1) and (2), we get:

Thus, the probability density function of T is given by:

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