※ 引述《CCZR (阿翔)》之銘言：
: Let the number of jobs arriving at a shop in a 1-hour period
: be a possion random variable N with mean m=4
: Each job requires Xi seconds to complete, where Xj's are independent
: and identically distributed random variables that are equal to 3 minutes
^^^^^^^^^
: or 6 minutes with equal Pr.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
這裡給你Xi|N的分配了
: Find the Pr generating funtion E[z^w]
^^^^^^
用z這個符號比較容易產生誤解...
很容易聯想成跟標準常態分配有關的東西
所以我自己把他改成求E(S^W)了 @@"
而且W題目沒註明是什麼 , 我想 W = X +X + ... +X 吧
1 2 N
下面如果有看不懂的再推文問吧~
iid
Xi|N ~ x 3 6
f(x) 0.5 0.5
W X1+X2+...+Xn X1 X2 Xn
E(S |N=n) = E(S ) = E(S )E(S )...E(S )
3 6 3 6 3 6
= (0.5S +0.5S )(0.5S +0.5S )...(0.5S +0.5S )
3 6 n
= (0.5S +0.5S )
W W 3 6 N
E( S ) = EE( S | N) = E(0.5S +0.5S ) = ...
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