作者pushfish (听天使在呢喃)
看板Grad-ProbAsk
标题Re: [商管] [统计]-逢甲91-统计与精算-动差母函数 …
时间Tue Nov 17 13:31:14 2009
※ 引述《jackoyu (伟下列资料正确填写并回숩》之铭言：
: 1.
: N ~ Poisson(λ=5)
: Xi's ~Exp(λ=3)
: S=X1+.....+XN
: Xi, N 独立
: 求 the monment generating function of S.
: 拜托强者，帮忙解答一下疑问，谢谢!!
双重期望值定理+指数分配可加性
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.
: 这题要怎麽做呢?是要用齐一性检定吗? 还是 ..... 谢谢!!
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) 我的神兵不见了 没法算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 为真[p=p'])
有错请指正 谢谢~~
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