2022 CJC P2 Q7
2022 CJC P2 Q7
7 marks
Prelims
The probability distribution for the random variable \(X\) is shown in the table.
| \(x\) | \(-1\) | \(0\) | \(1\) | \(2\) |
|---|---|---|---|---|
| \(\mathrm{P}(X=x)\) | \(p\) | \(\frac{1}{5}\) | \(q\) | \(\frac{1}{5}\) |
Another random variable \(Y\) is defined by \(Y=2{{X}_{1}}+{{X}_{2}}\), where \({{X}_{1}}\) and \({{X}_{2}}\) are independent observations of \(X\).
- Given that \(\mathrm{P}\left( Y=4 \right)=\frac{3}{25}\), find the values of \(p\) and \(q\).[3]
- Find \(\mathrm{E}\left( X \right)\) and \(\mathrm{Var}\left( X \right)\).[2]
- Find \(\mathrm{Var}\left( Y \right)\).[2]
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Answer:(i) \({p = \frac{1}{5}}\), \({q = \frac{2}{5}}\) (ii) \({\mathrm{E}(X) = \frac{3}{5}}\), \({\mathrm{Var}(X) = \frac{26}{25}}\) (iii) \({\mathrm{Var}(Y) = \frac{26}{5}}\)
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