MA2102

Probability and Statistics

Lecture-19

Theorem: Let $X$ is a random variable with $CDF$ $F_X(x)$, then $Y=F_X(X)\sim U[0,1]$

proof: $CDF$ of $Y$, $S_Y=[0,1]$    ($\because$ $0\le F_X(x)\le 1$)

for $0\le y\le1$, $F_Y(y)=P(Y\le y)$

                                      $=P(F_X(X)\le y)$