Dear All.

I have read in somewhere that if f is non decreasing function then

$\displaystyle p(X > \lambda) = p(f(X)>f( \lambda))$, and even somewhere it is written

$\displaystyle p(X > \lambda) \le p(f(X)>f( \lambda))$.

My question is this how this inequality is true, and which inequality is correct?

Can some explain in detail.

Regards.