grandes-ecoles 2025 QI.1

grandes-ecoles · France · x-ens-maths-c__mp Discrete Probability Distributions Properties of Named Discrete Distributions (Non-Binomial)

For $N = 1$, among random variables with usual distributions, give without justification one example of a random variable satisfying (8) and two examples of random variables not satisfying (8), where (8) states $\mathbb{P}(|X_n| \leq K) = 1$ for some constant $K \geq 1$, with $\mathbb{E}[X_n] = 0$ and $\operatorname{Var}(X_n) \leq 1$.

For $N = 1$, among random variables with usual distributions, give without justification one example of a random variable satisfying (8) and two examples of random variables not satisfying (8), where (8) states $\mathbb{P}(|X_n| \leq K) = 1$ for some constant $K \geq 1$, with $\mathbb{E}[X_n] = 0$ and $\operatorname{Var}(X_n) \leq 1$.

Paper Questions

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