"ZHANG Yan" <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > Suppose X,Y,Z are postive random variable, the pdf are given as f_X(t), > f_Y(t), f_Z(t). and > > Z=min(X, Y) >
In this you are assuming that X and Y are independent. > I know the following method to derive the cdf of Z. > > P(Z<t)=P(min(X,Y)<t)= 1- ( 1 - P( X<t ) )( 1 - P(Y<t) ). > > I am wondering how to evaluate it by using conditonal distribution. > > P(Z<t) = P( min(X, Y) < t ) = 1-P( min(X, Y) > t ) = 1 - [ P( X<t; X<Y) + > P( Y<t; Y<X)] > > is this correct and how to proceeding?Thanks. Actually, P( min(X, Y) < t ) =P( X<t; X<Y) + P( Y<t; Y<X) P( min(X, Y) > t ) =P( X>t; X<Y) + P( Y>t; Y<X) Thanks Sapsi . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
