选择题
5.设X，Y相互独立，且都服从参数为λ的指数分布，下列结论正确的是( )．
【正确答案】
C
【答案解析】因为X～E(λ)，Y～E(λ)，所以Fx(x)=
令Z=min{X，Y)，则Fz(z)=P{Z≤z}=1-P{Z＞z}=1一P{X＞z，Y＞z} =1一P{X＞z}P{Y＞z}=1一[1一P(X≤z}].[1一P{Y≤z}] =1一[1一Fx(z)].[1一Fy(z)]当z＜0时，Fz(z)=0；当z≥0时，Fz(z)=1一e-2λz．于是Fz(z)=
令Z=min{X，Y)，则Fz(z)=P{Z≤z}=1-P{Z＞z}=1一P{X＞z，Y＞z} =1一P{X＞z}P{Y＞z}=1一[1一P(X≤z}].[1一P{Y≤z}] =1一[1一Fx(z)].[1一Fy(z)]当z＜0时，Fz(z)=0；当z≥0时，Fz(z)=1一e-2λz．于是Fz(z)=