Question: 2. Let $X_{1}, X_{2}, ldots, X_{n}$ be a random sample from $X$ which follows an exponential distribution with parameter $theta$. a. Show that $bar{X}$ is

$2. Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample from$

2. Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample from $X$ which follows an exponential distribution with parameter $\theta$. a. Show that $\bar{X}$ is consistent estimator of $\theta$. (18) b. Show that $\bar{X}$ is sufficient statistics of $\theta$. c. Find the mean and the variance of $X$. SP.DL.1971

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