grandes-ecoles 2021 Q40

grandes-ecoles · France · centrale-maths2__psi Hypergeometric Distribution

Let $X$ be a random variable following the distribution $\mathcal{H}(n, p, A)$. We fix $n$ and $p$. We have shown that $$\lim_{A \to +\infty} \mathbb{P}(X = k) = \binom{n}{k} p^k (1-p)^{n-k}.$$ Interpret this result in connection with those obtained for the expectation and variance of $Y$.

Let $X$ be a random variable following the distribution $\mathcal{H}(n, p, A)$. We fix $n$ and $p$. We have shown that
$$\lim_{A \to +\infty} \mathbb{P}(X = k) = \binom{n}{k} p^k (1-p)^{n-k}.$$
Interpret this result in connection with those obtained for the expectation and variance of $Y$.

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