2022 NJC P2 Q8

2022 NJC P2 Q8

7 marks
Prelims

The table shows the probability distribution of a discrete random variable \(Y\).

\(y\)\(-1\)\(0\)\(1\)\(2\)\(3\)
\(\mathrm{P}(Y = y)\)\(\frac{32}{81}\)\(a\)\(\frac{8}{27}\)\(b\)\(c\)
  1. Given that \(\mathrm{E}\left( \left| Y-3 \right| \right)=\frac{232}{81}\), show that \(2b+3c=\frac{19}{81}\).[3]
  2. Given further that \(\mathrm{Var}\left( Y \right)=\frac{7736}{6561}\), find the values of \(a\), \(b\) and \(c\) in rational form.[3]
  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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