[商管] [統計]-高應大97-金資所

[aiaorry (我不想皺眉頭)]

If X and Y are joint normal with μx=1, μy= -1, σx=2, σy=1 and correlation
ρ= -0.7,

1. Calculate fx(x) and fy(y), the marginal p.d.f. of random variables X and Y
   respectively.

2. Evaluate the conditonal mean and conditonal variance of Y given X=x.

3. If Z1 = X+Y , Z2 = 3X-Y. Evaluate the correlation between Z1 and Z2.


這種題目的邊際分配是不是就不獨立了呢?!

該怎麼計算呢?!

謝謝


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推 goshfju:硬算 jpdf 積分下去 = = 或是你知道 jmgf 也 OK
→ goshfju:看配分吧 1. X~N(μx,σx^2) , Y~N(μy,σy)
→ goshfju:2.也是硬算 Y|X=x~N(μy+ρσy(x-μx)/σx,σy^2(1-ρ^2))
→ goshfju:3. 應該就容易多了~ 照相關係數的定義去算
→ goshfju:Y~N(μy,σy^2) 上面打錯了