grandes-ecoles 2025 Q23

grandes-ecoles · France · mines-ponts-maths2__psi Discrete Random Variables Existence of Expectation or Moments

Justify that for all $n \geq 0$, the random variables $\tilde { S } _ { n } , \tilde { I } _ { n }$ and $\tilde { R } _ { n }$ as well as the random variables $\Delta \tilde { S } _ { n } , \Delta \tilde { I } _ { n }$ and $\Delta \tilde { R } _ { n }$, have finite expectation.
Here $\Delta U_n = U_{n+1} - U_n$ and the random variables take values in $\{0, \ldots, M\}$.

Justify that for all $n \geq 0$, the random variables $\tilde { S } _ { n } , \tilde { I } _ { n }$ and $\tilde { R } _ { n }$ as well as the random variables $\Delta \tilde { S } _ { n } , \Delta \tilde { I } _ { n }$ and $\Delta \tilde { R } _ { n }$, have finite expectation.

Here $\Delta U_n = U_{n+1} - U_n$ and the random variables take values in $\{0, \ldots, M\}$.

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