[問題] Hogg的習題問題
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^^|| 試了幾個方法都只推得 <= 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.
這題我自己有做 但是跟解答的答案不一樣 但是我又覺得自己沒錯XD
所以想請教大家～
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曉園)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"的部份要怎麼處理＠＠
謝謝～
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