[機統] 隨機過程
Suppose that x1,x2,x3... are independent and identically ditributed
with Pr{xk=±1}=1/2 , Let N be independent of x1,x2, ...and follow the
geometric probability mass function
Pr(k)=α(1-α)^k for k =0 ,1...
where 0<α<1 Form the Random sum Z =x1+x2+....+xn
求 E(Z) , Var(Z) ,E(Z^3) , E(Z^4)
我有算了一下E(Z)=0, VAR(Z)= (1-α)/α
但是我不會算E(Z^3) 和 E(Z^4)
我有想過是否因為獨立可以將E(Z^3)=E(Z^2)*E(Z)
但是在E(Z^4)答案就會跟解答不同了
解答:E(Z^3)=0
E(Z^4)=[(1-α)*(6-α)]/α^2
請會的人教我一下 謝謝!!
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◆ From: 140.134.72.97
※ 編輯: dearwang 來自: 140.134.72.97 (05/05 11:48)
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