第1个回答 2012-05-20
令:Z=min{X, Y}.
则对于任意z, 有: P{Z<=z} = 1 - P{Z>z}= 1- P{X>z, Y>z} = 1 - P{X>z} *P{Y>z) . (1)
又P{a<Z<=b } = P{Z<b} - P{Z<a} ( 用(1) )
={1 - P{X>b} *P{Y>b } - {1 - P{X>a} *P{Y>a}
= P{X>a} *P{Y>a} - P{X>b} *P{Y>b }
=[P{X>a}]^2- [P{X>b}]^2 ( 由于同分布, P{X>a}= P{Y>a},P{X>b}= P{Y>b} )