[問題] 請問幾個問題
1.Consider the probability distribution of a bivariate discrete variable (X,Y)
may be represented as follows.
y1 y2 ... ym
x1 p11 p12 ... p1m p1.
x2 p21 p22 ... p2m p2.
...xn pn1 pn2 ... pnm pn.
p.1 p.2 p.m
Prove that if every row is proportional to any other row, then X and Y are
independent.
如果我定義p21=r2*p11, p22=r2*p12, ..., p2m=r2*p1m
...
pn1=rn*p11, pn2=rn*p12, ..., pnm=rn*p1m
讓every row is proportional to any other row
=>p2.=r2(p11+p12+...+p1m)=r2*p1.
...
pn.=rn(p11+p12+...+p1m)=rn*p1.
=>p.1=p11(1+r2+...+rn)
...
p.m=p1m(1+r2+...+rn)
然後我就卡住了...
2.Suppose that X1,...,Xn from a random sample of size n from the uniform
distribution on the interval (0,1) and that Yn=max{X1,...,Xn}. Find the
smallest value of n such that
P[Yn>=0.99]>=0.95
我的想法是先找出Yn的pdf
再代入P[Yn>=0.99]>=0.95
求出最小的n
不知道有沒有更快的方法?
煩請指教~感謝~~~
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※ 編輯: warep 來自: 220.229.67.228 (09/23 16:03)
※ 編輯: warep 來自: 220.229.67.228 (09/23 16:48)
※ 編輯: warep 來自: 220.229.67.228 (09/23 17:09)
※ 編輯: warep 來自: 220.229.67.228 (09/24 07:17)
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