One hundred items are simultaneously put on a life test. Suppose the lifetimes
of the individual items are independent exponential random variables with mean 200 hours. The test will end when there have been a total of 5 failures. If T is the time at which the test ends,

(a) Find E[T].
(b) Find Var(T).

a)

b)

Step-by-step explanation:

Given:

The lifetimes of the individual items are independent exponential random variables.

Mean = 200 hours.

Assume, Ti be the time between ( )st and the failures. Then, the are independent with being exponential with rate

Therefore,

a)

The variance is given by,

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