If $XIf $X$ and $Y$ two random varible with 
$$X\leq Y$$ then why $$F_X(x)\geq F_Y(y)$$
I have founded in paper.

then 


Suppose you know that if $A$ is true then so is $B.$ In that case $\Pr(A) \le \Pr(B).$
You have $X\le Y$ with probability $1.$
If $Y\le x$ then $X\le x.$
Therefore $\Pr(Y\le x) \le \Pr(X\le x).$
I.e. $F_Y(x) \le F_X(x).$
