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！！
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 219.84.181.137