grandes-ecoles 2024 Q11

grandes-ecoles · France · mines-ponts-maths2__mp Discrete Probability Distributions Proof of Probabilistic Inequalities or Bounds

Let $X$ be a random variable defined on a probability space $(\Omega , \mathcal{A} , \mathbf{P})$ with values in $\mathbf{N}$ and admitting an expectation $\mathbf{E}(X)$ and a variance $\mathbf{V}(X)$. Show that $\mathbf{P}(X > 0) \leq \mathbf{E}(X)$.

Let $X$ be a random variable defined on a probability space $(\Omega , \mathcal{A} , \mathbf{P})$ with values in $\mathbf{N}$ and admitting an expectation $\mathbf{E}(X)$ and a variance $\mathbf{V}(X)$.\\
Show that $\mathbf{P}(X > 0) \leq \mathbf{E}(X)$.

Paper Questions

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