※ [本文轉錄自 FCU_Talk 看板]
作者: janyfor (妳哪位ㄚ) 看板: FCU_Talk
標題: [考題] [機率論][林秀峰][952期末考]
時間: Sun Jul 8 20:40:42 2007
一、
Suppose that an average of 30 customers per hour arrive at a shop in
accordance with a Possion process.What is the probability that the shpkeer
will wait more 5 minutues before both of the first two customers customers
arriver？
二、
Let X and Y have the joint p.m.f
f(x,y) = 1/3 for (x,y) = (0,1) , (1,0) , (2,1)
1. Find cov(X,Y) =？
2. Are X and Y independent？
三、
Let the joint p.m.f, f(x,y) of X and Y be given by the following
(x,y) ║ f(x,y)
═══╬═════
(1,1) ║ 3/8
║
(2,1) ║ 1/8
║
(1,2) ║ 1/8
║
(2,2) ║ 3/8
Find the least square regression line L
四、
Roll a pair of four-side dice for which the outcome is 1,2,3 or 4 on each
dice. Let X donote the smaller and Y the larger outcome on the dice.
1. Find the joint p.m.f of X and Y
2. Find E[Y|X=2] =？
五、
If X1,X2....Xn are observation of a random sample size of n from the
Normal distribution N(μ,σ^2). Show that the sample mean
╴
Xn = (X1+X2+...+Xn)/n is N(μ,(σ^2)/n)
六、
State the following theorems
1. Chebyshev's Inequality
2. Law of Large Numbers
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