2024 EJC P2 Q7
2024 EJC P2 Q7
6 marks
Prelims
A random variable \(X\) has the probability distribution given in the following table.
| \(x\) | \(1\) | \(2\) | \(3\) | \(4\) |
|---|---|---|---|---|
| \(\mathrm{P}(X = x)\) | \(0.4\) | \(0.3\) | \(0.2\) | \(0.1\) |
- Find \(\mathrm{Var}\left( X \right)\) and show that \(\mathrm{Var}\left( 3X-2 \right)=39.96\).[3]
- The mean of \(40\) independent observations of \(X\) is denoted by \(M\). Find an approximate value for \(\mathrm{P}\left( M>3 \right)\).[3]
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Answer:(a) \({4.44}\) (b) \({0.115}\) (\(3\) sofa)
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