※ [本文转录自 FCU_Talk 看板] 作者: janyfor (你哪位ㄚ) 看板: FCU_Talk 标题: [考题] [机率论][林秀峰][952期末考] 时间: 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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