I'm just wondering how to prove that $$P ( X < F^{-1} (y)) \leq y $$ where $F^{-1} (y) = \inf \{x: F(x) \geq y \}$ and $F$ is CDF of random variable X.
I'm sure this is pretty simple, but I can't figure this thing out.
I'm just wondering how to prove that $$P ( X < F^{-1} (y)) \leq y $$ where $F^{-1} (y) = \inf \{x: F(x) \geq y \}$ and $F$ is CDF of random variable X.
I'm sure this is pretty simple, but I can't figure this thing out.