grandes-ecoles 2020 Q37

grandes-ecoles · France · centrale-maths2__pc Discrete Random Variables Existence of Expectation or Moments

We fix a real random variable $X : \Omega \rightarrow \mathbb { R }$, whose image $X ( \Omega )$ is a countable set. Let $k \in \mathbb { N } ^ { * }$. Deduce from the previous questions that if $\phi _ { X }$ is of class $C ^ { 2 k }$ on $\mathbb { R }$, then $X$ admits a moment of order $2 k$.

We fix a real random variable $X : \Omega \rightarrow \mathbb { R }$, whose image $X ( \Omega )$ is a countable set.\\
Let $k \in \mathbb { N } ^ { * }$. Deduce from the previous questions that if $\phi _ { X }$ is of class $C ^ { 2 k }$ on $\mathbb { R }$, then $X$ admits a moment of order $2 k$.

Paper Questions

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