(Solution Library) Let X have a gamma distribution with α=4 and β=θ>0. Find the Fisher information of one observation I(θ). If X_1, X_2,
Question: Let \(X\) have a gamma distribution with \(\alpha=4\) and \(\beta=\theta>0\).
- Find the Fisher information of one observation \(I(\theta)\).
- If \(X_{1}, X_{2}, \ldots, X_{n}\) is a random sample from this distribution, show that the MLE is an efficient estimator of \(\theta\).
Deliverable: Word Document 
![[Step-by-Step] Given f(x ; θ)=1 / θ,](/images/solutions/MC-solution-library-46338.jpg "[Step-by-Step] Given f(x ; θ)=1 / θ, 00, formally")
[Step-by-Step] Given f(x ; θ)=1 / θ, 00, formally
(Solution Library) Let X ~ Bin;(10, p), p ∈ 1/4, 1/2. The
(Solution Library) If X_1, X_2 is a random sample of size 2 from
(Solution Library) Let X have a Poisson distribution with mean θ.
![[Solution Library] If X_1, X_2, ..., X_n](/images/solutions/MC-solution-library-46342.jpg "[Solution Library] If X_1, X_2, ..., X_n is a random sample from a")
[Solution Library] If X_1, X_2, ..., X_n is a random sample from a
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