作者buttermilk (脱脂牛奶)
看板Statistics
标题Re: [问题] 一题相关系数的问题
时间Fri Apr 20 13:31:29 2007
※ 引述《[email protected] (老怪物)》之铭言：
: ※ 引述《[email protected] (脱脂牛奶)》之铭言：
: > Let (σ_1)^2 = (σ_2)^2 = σ^2 be the common variance of X_1 and X_2 and
: > let p be the correlation coefficient of X_1 and X_2. Show that
: ^^ρ, not p.
Thanks for your correction.
: > P[│(X_1-μ_1) + (X_2-μ_2)│≧kσ]≦2(1+ρ)/k^2.
: Hint: Var(X_1+X_2) = ?
: > -------------------------------------------------------------------------
: > 我觉得应该是要利用Chebyshev's Inequality来做
: > 不过我就是不会写=.=
Thanks for your hint:)
Var(X_1+X_2) = Var(X_1) + Var(X_2) +
2 Cov(X_1,X_2)
( 我当初就是少了黄色这一项才算不出来 =.= )
= 2σ^2 + 2σ^2ρ
= 2σ^2(1+ρ)
E(X_1+X_2) = E(X_1) + E(X_2) = μ_1 + μ_2
Let Y = X_1 + X_2.
Then (σ_Y)^2 = 2σ^2(1+ρ).
By Chebyshev's Inequality, P[│(X_1-μ_1) + (X_2-μ_2)│≧kσ]≦2(1+ρ)/k^2.
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※ 编辑: buttermilk 来自: 203.64.26.246 (04/20 13:31)