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[Solved] Let X_1, X_2, ..., X_n be a random sample of size n from an exponential distribution with unknown mean of μ=θ. Show that the distribution

Question: Let $X_{1}, X_{2}, \ldots, X_{n}$ be a random sample of size $n$ from an exponential distribution with unknown mean of $\mu=\theta$.

Show that the distribution of $W=(2 / \theta) \sum_{i=1}^{n} X_{i}$ is $\chi^{2}(2 n)$. HINT: Find the moment-generating function of $W$.
Use W to construct a $100(1-\alpha )$ $\%$ confidence interval

for theta.

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[Solved] Let X_1, X_2, ..., X_n be a random sample of size n from an exponential distribution with unknown mean of μ=θ. Show that the distribution

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