2022 CJC P2 Q7
The probability distribution for the random variable $X$ is shown in the table.
Another random variable $Y$ is defined by $Y=2{{X}_{1}}+{{X}_{2}}$, where ${{X}_{1}}$ and ${{X}_{2}}$ are independent observations of $X$.
(i)
Given that $\text{P}\left( Y=4 \right)=\frac{3}{25}$, find the values of $p$ and $q$.
[3]
(ii)
Find $\text{E}\left( X \right)$ and $\text{Var}\left( X \right)$.
[2]
(iii)
Find $\text{Var}\left( Y \right)$.
[2]
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