Question 4 Point Estimation ( 30 points) Assume the lifetime (in mon.pdf

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Question 4: Point Estimation ( 30 points) Assume the lifetime (in months) of batteries is modeled as an exponential random variable with parameter - The probability density function of the random variable is Let (X1,,Xn) be a random sample f(x)=1ex/,x(0,) (a) [10 pts] What is the maximum likelihood estimator (A, (b) [ [pts] Is the estimator unbiased? Explain. (c) [12pts] Suppose =1. Use the central limit theorem to approximate the probability your estimator.

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