Aufgabe \( 3(6 \text { Punkte }): \) The random variable \( X \) has values in \( \mathbb{N} \) and its expected value \( E(X)<\infty \) exists. Show \( (3 \mathrm{P.}) \)
$$ E(X)=\sum \limits_{n=1}^{\infty} P(X \geq n) $$
Do you find a similar relation between expected value and distribution function for a nonnegative random variable which is absolutely continuous? \( (3 \mathrm{P.}) \) (expected value \( = \) Erwartungswert, absolutely continuous \( = \) absolut stetig
Ich weiß leider gar nicht, wie ich das machen soll