作者hi123 (hi123)
看板Statistics
标题[问题] Hogg的习题问题
时间Tue Dec 4 22:45:46 2007
是第6版的
2.4.11
Let σ1^2=σ2^2=σ^2 be thecommon variance of X1 and X2
and let ρ be the correlation coefficient of X1 and X2.
Show that P[|(X1-μ1)+(X2-μ2)| >= kσ] <= 2(1+ρ)/k^2
可否提示我一下^^|| 试了几个方法都只推得 <= 1/k^2
2.5.11
Two line segments, each of length two units, are placed
along the x-axis. The midpoint of the first is between
x=0 and x=14 and that of the second is between x=6 and
x=20. Assuming independence and uniform distributions for
these midpoints, find the probability that the line
segments overlap.
这题我自己有做 但是跟解答的答案不一样 但是我又觉得自己没错XD
所以想请教大家～
我的作法是：X～U(0,14), Y～U(6,20), f(x,y)=1/14 * 1/14 = 1/196
所求 = P(|X-Y| < 2) = P(-2 < X-Y < 2)
= (4*6 + 4*4/2) / 196
= 8/49
答案(form晓园)是16/49
2.6.2
Let f(x,y,z) = exp[-(x+y+z)], x>0, y>0, z>0, zero elsewhere,
be the joint pdf of X, Y, Z. Compute P(X=Y<Z).
"X=Y"的部份要怎麽处理＠＠
谢谢～
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※ 编辑: hi123 来自: 58.99.57.41 (12/04 23:12)
1F：→ hi123:Introduction to mathematical statistics 忘了说sorry^^|| 12/04 23:14
2F：推 austinly:1. Chebysheve Inequality,P(|X-μ|>=ε)<=Var(X)/(ε^2) 12/05 01:03
3F：→ austinly:2. 题目要求共同区域的机率应该为P(6<X,Y<14) 12/05 01:05