grandes-ecoles 2018 Q7

grandes-ecoles · France · centrale-maths1__official Discrete Random Variables Expectation of a Function of a Discrete Random Variable

Let $X : \Omega \rightarrow \mathbb{R}$ be a real-valued random variable. Let $(A_{1}, \ldots, A_{m})$ be a complete system of events with non-zero probabilities. Show that
$$\mathbb{E}(X) = \sum_{i=1}^{m} \mathbb{P}(A_{i}) \cdot \mathbb{E}(X \mid A_{i})$$

Let $X : \Omega \rightarrow \mathbb{R}$ be a real-valued random variable. Let $(A_{1}, \ldots, A_{m})$ be a complete system of events with non-zero probabilities. Show that

$$\mathbb{E}(X) = \sum_{i=1}^{m} \mathbb{P}(A_{i}) \cdot \mathbb{E}(X \mid A_{i})$$

Paper Questions

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