※ 引述《jackoyu (偉下列資料正確填寫並回숩》之銘言：
: 1.
: N ~ Poisson(λ=5)
: Xi's ~Exp(λ=3)
: S=X1+.....+XN
: Xi, N 獨立
: 求 the monment generating function of S.
: 拜託強者，幫忙解答一下疑問，謝謝!!
雙重期望值定理+指數分配可加性
Ms(t)=E(e^st)=E[E(e^t*ΣXi l N)]=E[E(e^X1t+.....+e^Xnt l N )]
=E[(1-1/3*t)^-n)]
=(1-1/3*t)^-n)*e^-5*5^n/n! n=0,1,2......
: 2.
: You suspect one of the die have been modified. You roll the suspected
: die 50 times. The observed distribution is provided below,
: Value(x) 1 2 3 4 5 6
: observed 13 12 10 8 4 3
: let p=P(X=1/6),test H0:p<= 1/6 H1:p> 1/6
: (a) find the exact p-value
: (b) Use normal approximayion to find the p-value
: (c) Find a rejection region for test at α=0.05,and the power function.
: 這題要怎麼做呢?是要用齊一性檢定嗎? 還是 ..... 謝謝!!
A.
X bar=2.74 EX=3.5
P-value=(x<=2.74)
B. X bar=2.74 E(Xbar) =3.5 V(Xbar)=6^2-1 / 12= 35/12*1/50
P(X<=2.74)=P(X<2.74+0.5) 我的神兵不見了 沒法算T_T
C.
k=3.5-Z(0.025)*35/12*1/50 =3.5-1.96*35/12*1/50
power=(X bar<=k l Ha 為真[p=p'])
有錯請指正 謝謝~~
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