grandes-ecoles 2020 Q33

grandes-ecoles · France · centrale-maths2__pc Continuous Probability Distributions and Random Variables Expectation and Moment Inequality Proof

We fix a real random variable $X : \Omega \rightarrow \mathbb { R }$, whose image $X ( \Omega )$ is a countable set, with $X ( \Omega ) = \left\{ x _ { n } , n \in \mathbb { N } \right\}$ and $a _ { n } = \mathbb { P } \left( X = x _ { n } \right)$. We assume that $\phi _ { X }$ is of class $C ^ { 2 }$ on $\mathbb { R }$. Using the results of Q31 and Q32, deduce that $X$ admits a moment of order 2.

We fix a real random variable $X : \Omega \rightarrow \mathbb { R }$, whose image $X ( \Omega )$ is a countable set, with $X ( \Omega ) = \left\{ x _ { n } , n \in \mathbb { N } \right\}$ and $a _ { n } = \mathbb { P } \left( X = x _ { n } \right)$.\\
We assume that $\phi _ { X }$ is of class $C ^ { 2 }$ on $\mathbb { R }$.\\
Using the results of Q31 and Q32, deduce that $X$ admits a moment of order 2.

Paper Questions

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