2015-01概率统计试卷+答案 (2)

1??1 四 计算题1. ∵X～E(?) ∴E(X)= 矩估计： E(X)?X ?X?似然函数L(?)??nn?ei?1n??xi=

?en???xii?1n,

ndlnL?n/???xi?0 故lnL?nln????xi,d?i?1i?1n??n/??xi?1i?1/X

?1?,x2?y2?12. f(x,y)???

?其它?0,??fx(x)?????1?x2121?x2?dy?f(x,y)dy=??2???1?x?0????1?x?1其他

fy(y)?????1?y2121?y2??dx?f(x,y)dx ????1?y2?0?1?x2?1?y?1其他

E(X)??dx??111?1?x2?xdy?0E(Y)??dx??111?x21?1?x2?ydy?0E(XY)??dx??111?x21?1?x2?xydy?0，cov(X,Y)?E(XY)?E(X)E(Y)?0

?XY?0

?对任意x,y,f(x,y)?fX(x)?fY(y),?X与Y不独立.

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