2022 NJC P2 Q8
2022 NJC P2 Q8
7 marks
Prelims
The table shows the probability distribution of a discrete random variable \(Y\).
| \(y\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) |
|---|---|---|---|---|---|
| \(\mathrm{P}(Y = y)\) | \(\frac{32}{81}\) | \(a\) | \(\frac{8}{27}\) | \(b\) | \(c\) |
- Given that \(\mathrm{E}\left( \left| Y-3 \right| \right)=\frac{232}{81}\), show that \(2b+3c=\frac{19}{81}\).[3]
- Given further that \(\mathrm{Var}\left( Y \right)=\frac{7736}{6561}\), find the values of \(a\), \(b\) and \(c\) in rational form.[3]
- Justify if \(Y\) follows a binomial distribution.[1]
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Answer:(ii) \(a=\frac{16}{81}\), \(b=\frac{8}{81}\), \(c=\frac{1}{81}\) (iii) \(Y\) does not follow a binomial distribution since it can possibly take a value of \(-1\) which is not permissible in a binomial distribution that counts the number of success.
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