grandes-ecoles 2022 Q19

grandes-ecoles · France · centrale-maths1__psi Discrete Probability Distributions Proof of Distributional Properties or Symmetry

Let $X$ and $Y$ be two independent real random variables, each following the distribution $\mathcal { R }$ (where $X ( \Omega ) = \{ - 1,1 \}$, $\mathbb { P } ( X = - 1 ) = \mathbb { P } ( X = 1 ) = \frac { 1 } { 2 }$). Determine the distribution of their product $X Y$.

Let $X$ and $Y$ be two independent real random variables, each following the distribution $\mathcal { R }$ (where $X ( \Omega ) = \{ - 1,1 \}$, $\mathbb { P } ( X = - 1 ) = \mathbb { P } ( X = 1 ) = \frac { 1 } { 2 }$). Determine the distribution of their product $X Y$.

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