$X$,$Y$ are independent random variables, whose density function is $f(x,y)$.
To get the Probability of $X
$P(X
$f(x,y)=f_{X}(x)f_{Y}(y)$
$\int_{-\infty}^ydx\int_{-\infty}^{+\infty}f(x,y)dy=\int_{-\infty}^ydx\int_{-\infty}^{+\infty}f_{X}(x)f_{Y}(y)dy=\int_{-\infty}^y[f_{X}(x)\int_{-\infty}^{+\infty}f_{Y}(y)dy]dx=\int_{-\infty}^y[f_{X}(x)\int_{-\infty}^{+\infty}f_{Y}(y)dy]dx=\int_{-\infty}^yf_{X}(x)dx=F_X(y)$
But we know that
$P(X
What's wrong with my calculation?