Suppose that X1,...,Xn form a random sample

Chapter 7, Problem 12

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QUESTION:

Suppose that X1,...,Xn form a random sample from an exponential distribution for which the value of the parameter is unknown. Show that the sequence of M.L.E.s of is a consistent sequence.

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QUESTION:

Suppose that X1,...,Xn form a random sample from an exponential distribution for which the value of the parameter is unknown. Show that the sequence of M.L.E.s of is a consistent sequence.

ANSWER:

Step 1 of 3

We can prove  by using the law of large numbers.

The expected value of a random variable with exponential distribution is,

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