grandes-ecoles 2018 Q32

grandes-ecoles · France · centrale-maths1__official Continuous Probability Distributions and Random Variables Probability Inequality and Tail Bound Proof

Complete the proof of inequality
$$\mathbb{P}(X \in C) \cdot \mathbb{E}\left(\exp\left(\frac{1}{8}d(X, C)^{2}\right)\right) \leqslant 1 \tag{II.1}$$

Complete the proof of inequality

$$\mathbb{P}(X \in C) \cdot \mathbb{E}\left(\exp\left(\frac{1}{8}d(X, C)^{2}\right)\right) \leqslant 1 \tag{II.1}$$