Question: Let the random variables in the sequence (left{X_{n}ight}) be iid with a gamma density having parameters (alpha=2) and (beta=3). (a) What is the probability density

Let the random variables in the sequence $\left\{X_{n}ight\}$ be iid with a gamma density having parameters $\alpha=2$ and $\beta=3$.

(a) What is the probability density for $\bar{X}_{n}$ ?

(b) What is the asymptotic probability density for $\bar{X}_{n}$ ?

(c) Plot the actual versus asymptotic probability density for $\bar{X}_{n}$ when $n=10$.

(d) Repeat

(c) for $n=40$. Interpret the graphs in

(c) and

(d) in terms of asymptotic theory.

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