作者msu (do my best)
看板Grad-ProbAsk
標題[商管] [統計]-離散型機率分配
時間Thu Dec 10 13:20:34 2009
Let Sk=X1+X2+~~~+XK,WHERE Xi's independent Bernoullirandom variable with mean
parameter p and K is another discrete random variable independent of Xi's
(1)If K=k ,is anconstant,show that Sk is a binomial random variable with
parameter k and p
(2)If K is gerometrically distributed random with parameter g,show that
Sk is gerometrically distributed random variable and find its parameter
請問這一題如何解呢?
感謝各位^^
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 118.167.232.253
1F：推 hchs31705:第一題是證明伯努力相加會變成二項 用動差母函數證? 12/10 13:53
2F：→ hchs31705:S|k~b(k,p)且k~g(g) 求出f(S,k)=f(k)*f(S|k) 再把k加掉 12/10 13:58
3F：→ hchs31705:上面是第二題 12/10 13:58
4F：→ msu:...還是證不太出來@@ 12/10 16:16
5F：推 hchs31705:哪一提@@ X相加.動差母相乘=(q+pe^t)^k=b(k.p)的動差母 12/10 16:28
6F：推 hchs31705:X獨立可以拆開且由動差母函數之唯一性得到 12/10 16:30
7F：→ msu:我懂了 感謝^^ 12/11 03:09