Re: [理工] [機率]-台大96-生醫電子所

[jasonkuo515 (孝仔)]

※ 引述《dohard (最近很忙 請來電^^)》之銘言：
: 2.For two random variables X and Y with covariance Cov(X,Y)=0
:   Find the correlation p(X+Y,X-Y).
Cov(X+Y,X-Y)=E[(X+Y)(X-Y)]-E[X+Y]E[X-Y]

            =E[X^2-Y^2]-(E[X]+E[Y])(E[X]-E[Y])

            =E[X^2]-E[Y^2]-(E[X])^2+(E[Y])^2

            =Var[X]-Var[Y]


σ  ^2 =Var[X+Y]=Var[X]+Var[y]+2Cov(X,Y)
 x+y
                =Var[X]+Var[y]=σ  ^2
                                x-y

ρ(X+Y,X-Y)=Cov(X+Y,X-Y)/(σ  σ)
                           x+y x-y

           =Cov(X+Y,X-Y)/(Var[X]+Var[y])

           =(Var[X]-Var[Y])/(Var[X]+Var[Y])


: 3.For two random variables X and Y with joint probability density function
:            3/2(x^2+y^2) if 0<x<1 and 0<y<1
:    f(x,y)=
:            0              otherwise
:    Find f    (X1Y)
:          X1Y
          1             1
先求f(y)=∫f(x,y)dx=3/2∫(x^2+y^2)dx = 3/2y^2+1/2
          0             0

        = 3/2y^2+1/2  ,0<y<1


f(x∣y)=f(x,y)/f(y) ,0<x<1  0<y<1

:    謝謝
    不客氣

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◆ From: 140.112.7.59
→ jasonkuo515:你在計中PO 我在計中回XDDDD
※ 編輯: jasonkuo515     來自: 140.112.7.59         (02/23 18:54)
→ jasonkuo515:剛剛眼殘以為第一題要求Cov[X+Y,X-Y]所以沒算完...
→ Hank2005:correlation是E[XY]不是相關係數
→ jasonkuo515:真的假的!!
推 jamtu:真的  被唬爛了
→ jamtu:考試的時候真的很容易眼殘  QQ
推 jamtu:這一題原本是問correlation coefficient...