Let the random variables in the sequence (left{X_{n}ight}) be iid with a gamma density having parameters (alpha=2)

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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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Mathematical Statistics For Economics And Business

ISBN: 9781461450221

2nd Edition

Authors: Ron C.Mittelhammer

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Question Posted: Feb 28, 2024 02:01 AM

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Let the random variables in the sequence (left{X_{n}ight}) be iid with a gamma density having parameters (alpha=2)

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Analyzing Sequence of IID Gamma Distributed Variables a Probability Density of Sample Mean Actual For a sequence of iid gammadistributed variables Xi ...View the full answer

Mathematical Statistics For Economics And Business

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