Why is the function required to be monotonic here? I understand if the function is not monotonic the first equality would not hold true. But the second inequality will always hold true with respect to the first probability i.e
$$P(|X - \mu| \geq t) \leq \frac{E[f(|X-\mu|)]}{f(t)}$$
Did I do some mistake in my calculation? Elaboration of this slide would be nice.
