[商管] [統計]-離散型機率分配

[msu (do my best)]

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
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?
→ 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
→ hchs31705:上面是第二題
→ msu:...還是證不太出來@@
推 hchs31705:哪一提@@  X相加.動差母相乘=(q+pe^t)^k=b(k.p)的動差母
推 hchs31705:X獨立可以拆開且由動差母函數之唯一性得到
→ msu:我懂了 感謝^^