Consider the probability density function

Chapter 7, Problem 48E

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QUESTION:

Consider the probability density function \(f(x)=\frac{1}{\theta^{2}} x e^{-x / \theta}\),\(\quad 0 \leq x<\infty, \quad 0<\theta<\infty\)

Find the maximum likelihood estimator for \(\theta\).

Questions & Answers

QUESTION:

Consider the probability density function \(f(x)=\frac{1}{\theta^{2}} x e^{-x / \theta}\),\(\quad 0 \leq x<\infty, \quad 0<\theta<\infty\)

Find the maximum likelihood estimator for \(\theta\).

ANSWER:

Solution :

Step 1 of 1:

Our goal is:

We need to find the maximum likelihood estimator of .

Given  x>0, 0

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