Question: Under normal operating conditions the operating time until failure os a certain type of component has an exponential distribution for some > 0. Suppose that

Under normal operating conditions the operating time until failure os a certain type of component has an exponential distribution for some > 0. Suppose that the lifetimes of different components can be regarded to be independent of one another.

(1)The average lifetime of 20,000 components is found to be 10 days. Estimate the value of .

(2) Assuming the above exponential model with = 10% per day, let Nd be the number of components among the 20,000 that survive more that d days.

a. What is the distribution of Nd?

b. Find E[Nd].

c. Find SD(Nd).

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