1.Consider the following genetic(linkage) data model Type AA Aa aA aa Total probability (1+θ)/4 (1-θ)/4 (1-θ)/4 (1+θ)/4 1 Observed frequency n1 n2 n3 n4 n where θ(-1<=θ<=1) is the linkage parameter. a.Drive an equation which can be used to find the maximum likelibood ～ estimator (MLE) θ of θ. Find the MLE and also compute its mean and variance.　　　　　　　　　　　　　 ～ b.What is the (exact) distribution of θ? ～ c.Is θ the uniformly minimum variance unbiased estimate (UMVUE) of θ? 2.Let X1,X2... be a random sample of size n from a N(μ,σ^2) population. _ _ 1 n 2 1 n _ 2 √n(X-μ) Let X= ─ Σ Xi,S = ── Σ (Xi-X) , and Tn-1 = ───── 　　　　 n i=1 n-1 i=1 S _ Calculate the correlation Corr(X,Tn-1),and numerically evaluate this expression for n=3 and 4.You can use the fact that if Y ~ χ2(ν),then τ τ Γ(ν/2+τ) E( Y )= 2 ─────── , ν/2+τ> 0 ,Γ denote the gamma function. Γ(ν/2) 第一題是離散型的，但是完全不知道要怎麼下手也不知道怎麼去假設開始的條件 第二題也是在想T分配與X霸的關係轉換就快暈了，煩請有高手可以幫忙解答一下 ，謝謝！！ --

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