ThmDex – An index of mathematical definitions, results, and conjectures.

ThmDex – An index of mathematical definitions, results, and conjectures.

Formulation F12625 on R5282: Expectation of a random fraction need not equal fraction of expectations

F12625

Formulation 0

Let $X \in \text{Bernoulli}(1 / 2)$ be a D3999: Standard Bernoulli random boolean number.

Then

(1)	\begin{equation} \mathbb{E} \left( \frac{1}{1 + X} \right) = \frac{3}{4} \end{equation}
(2)	\begin{equation} \frac{1}{\mathbb{E}(1 + X)} = \frac{2}{3} \end{equation}