[商管] [統計] 94政大風管(精算組)
http://small.lib.nccu.edu.tw/exam/data/master/ins/ins94.pdf
想請教的是精算組統計2,4,5
_ _
2. Tn = (Xn - u) , where Xn and Sn^2 represent the mean and
---------- the variance of a random sample of size n
√(Sn^2/ (n-1)) from a distribution that is N(u, sigma^2).
Find the limiting distribution of Tn.
You are also require to justify your result.
我想到的的做法只有一半Orz，要麻煩高手指點了
(1) _
X - u
-------- d收斂至 N(0,1) by CLT
sigma/√n
(2) 應該是可以湊出一個東西用 WLLN p收斂到一個常數c，
前幾天算是1,結果現在覺得好像那天算錯，然後現在算不出來了。
然後(1)/(2), by slutzky, 知道 收斂到 N(0,1)/c = N(0,1/c^2)
順便借這題問一下96年精算組統計第二題(b)小題
http://small.lib.nccu.edu.tw/exam/data/master/ins/ins96.pdf
96年第二題(b)小題，問的是"分配",是t(n-1)
94年第二題，問的是"極限分配",是N
不知道我的認知有沒有錯誤，謝謝。
4.5.兩題就完全下不了手。
4.Let n(x) and N(x) be the p.d.f. and the distribution function
of a distribution that is N(0,1).
Let Y have truncated distribution with p.d.f. g(y)= n(y) , b < y < a
---------
N(a)-N(b)
zero elsewhere. Find E(Y).
5.If X1, X2 is a random sample from a distribution that is N(0,1)
find the joint p.d.f. of Y1=X1^2+X2^2 and Y2=X2
and the marginal p.d.f. of Y1
謝謝。
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