Statistics Solutions

[All Steps] [14] Suppose that Y 1 , Y 2 , ……, Y n denote a random sample from an exponentially distributed population with mean θ . Find the maximum

Question: [14] Suppose that Y 1 , Y 2 , ……, Y n denote a random sample from an exponentially distributed population with mean \[\theta \] . Find the maximum likelihood estimator (MLE) of the population variance \[{{\theta }^{2}}\] . Note that the probability density function for an exponential distribution is

\[\begin{aligned} & f(y)=\frac{1}{\theta }{{e}^{\frac{-y}{\theta }}},\text{ 0}<\text{y}<\infty \text{, }\theta >\text{0} \\ & \text{ 0, elsewhere}\text{. } \\ \end{aligned}\]

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