Re: [問題] 一題相關係數的問題

[buttermilk (脫脂牛奶)]

※ 引述《[e-mail] (老怪物)》之銘言：
: ※ 引述《[e-mail] (脫脂牛奶)》之銘言：
: > 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) = ?
: > -------------------------------------------------------------------------
: > 我覺得應該是要利用Chebyshev's Inequality來做
: > 不過我就是不會寫=.=

Thanks for your hint:)

Var(X_1+X_2) = Var(X_1) + Var(X_2) + 2 Cov(X_1,X_2)

( 我當初就是少了黃色這一項才算不出來 =.= )

             = 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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※ 編輯: buttermilk      來自: 203.64.26.246        (04/20 13:31)