作者goshagainfuc (...)
看板Statistics
标题[问题] 机率的问题
时间Wed Nov 22 00:46:10 2006
1.let X be random variable with probability mass function
n r n-r
P(X=r) = ( )p (1-p) , if r = 0,1,2,..,n. 0≦p≦1.
r
Find the pmfs of the random variables (a) Y=X^2 , and (b) Y=√X
2.show that E(Y-Φ(X))^2 is minimized by choosing Φ(X)=E(Y|X).
3.Let {An} be a sequence of events such that An → A as n→∞.
Show that P(An)→P(A) as n→∞
1.我是写
X=Y^2 => Y = √X
n √r n-√r
P (r) = P (√r) = ( )p (1-p) , for r = 0 , 1 , 4 , ... , n^2
Y X √r
X=√Y => Y = X^2
n r^2 n-r^2
P (r) = P (r^2) = ( )p (1-p) , for r = 0 , 1 , 2 , √3 , ... , √n
Y X r^2
有那麽简单吗?总觉得怪怪的@@""
2.好像是回归线的性质?直接算 E(Y-E(Y|X))^2 还有些头绪 但从E(Y-Φ(X))^2要变出
E(Y|X)真的弄不出来耶@@""
3.我对於这种看似理所当然的命题都不会证耶@@""是因为没修过高微的关系吗?
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1F：推 ym7226:1.不对喔再看看 2.展开看看 3.机率论最前面的东西吧 11/22 01:07
2F：推 TOOYA:1 你为什麽前面ab小题互换 後面又换回来?? 11/22 06:27
3F：推 TOOYA:2 减一项加一项E(Y|X)之後展开 中间项取E(.)=E(E(.|X))即可 11/22 06:36
4F：推 TOOYA:3 Bn=(A-An)∪(An-A) Bn->ψ as n→∞ imply what u want 11/22 06:40
5F：推 goshagainfuc:感谢 我再试看看 囧 11/22 18:22