[機統] Uniform變數變換的相關系數

[tokyo291 (工口工口)]

U is uniform(0,1) find Corr(U^2,sqrt(1-U^2))

(sqrt():開根號)

我是從基本開始作

                           Cov(U^2,sqrt(1-U^2))
Corr(U^2,sqrt(1-U^2))=-------------------------------
                      sqrt(Var(U^2))*sqrt(Var(1-U^2))

Cov(U^2,sqrt(1-U^2))=E(U^2*sqrt(1-U^2))-E(U^2)E(sqrt(1-U^2)))

                        1
其中E(U^2*sqrt(1-U^2))=∫u^2*sqrt(1-u^2)du這一段積分是想請教的地方
                        0

這個地方積分該如何做呢?

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