Suppose that certain electronic components have lifetimes that are exponentially distributed: f (t|τ) = (1/τ ) exp(−t/τ ), t ≥ 0. Five new components are put on test, the first one fails at 100 days, and no further observations are recorded.
a. What is the likelihood function of τ ?
b. What is the mle of τ ?
c. What is the sampling distribution of the mle?
d. What is the standard error of the mle?
(Hint: See Example A of Section 3.7.)
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