et X1, X2,..., Xn be a random sample of size n >3 from a normal distribution ith unknown mean μ and known variance equal to 2. Show that the maximum likelihood estimator of μ is ₁ = (1/n) Xt. Make sure to verify that û maximizes the log-likelihood function.

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A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

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A: Given: X1, X2, ‐‐‐‐,Xn~Poissonλ.    ⇒fx=e-λ.λxx!   Likelihood fuction:-      ⇒Lλ =e-nλλΣxiπ x!…

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A: For the given random variable X, its pdf is

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A: f(x)=2x ; 0&lt; x&lt; 1 n be the sample size

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Q: how that the variance of a geometric random variable X; is given by V ar(X) = q/p^2 .

A:

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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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A: Result: If X~N(0,1) then X2~χ2(1) χ2(n1)+χ2(n2)=χ2(n1+n2)  E(χ2(n))=n and V(χ2(n))=2n

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