grandes-ecoles 2022 Q26

grandes-ecoles · France · centrale-maths2__mp Continuous Probability Distributions and Random Variables Almost Sure Convergence and Random Series Properties

With the notation and setup of the previous questions (mutually independent Rademacher variables, $S_N = \sum_{n=0}^N X_n a_n$, events $B_j$), denote by $B$ the event $\bigcap_{J \in \mathbb{N}} \bigcup_{j \geqslant J} B_j$. Show the equality $\mathbb{P}(B) = 0$.

With the notation and setup of the previous questions (mutually independent Rademacher variables, $S_N = \sum_{n=0}^N X_n a_n$, events $B_j$), denote by $B$ the event $\bigcap_{J \in \mathbb{N}} \bigcup_{j \geqslant J} B_j$. Show the equality $\mathbb{P}(B) = 0$.

Paper Questions

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