The probability distribution of a discrete random variable $X$ is as follows:
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Find $\mathrm{Var}\left( X \right)$.
The random variable $Y$ is defined by $Y={{X}_{1}}-{{X}_{2}}$, where ${{X}_{1}}$, ${{X}_{2}}$ are two independent observations of $X$.
Find the probability distribution of $Y$.
Verify that $\mathrm{Var}\left( Y \right)=\mathrm{Var}\left( {{X}_{1}} \right)+\mathrm{Var}\left( {{X}_{2}} \right)$.

The probability distribution of a discrete random variable $X$ is as follows:

The random variable $Y$ is defined by $Y={{X}_{1}}-{{X}_{2}}$, where ${{X}_{1}}$, ${{X}_{2}}$ are two independent observations of $X$.

Find the probability distribution of $Y$.

Verify that $\mathrm{Var}\left( Y \right)=\mathrm{Var}\left( {{X}_{1}} \right)+\mathrm{Var}\left( {{X}_{2}} \right)$.

ACJC DRV Tutorial Q4

ACJC DRV Tutorial Q4

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