4 A random variable \(X\) has a rectangular distribution.
The mean of \(X\) is 3 and the variance of \(X\) is 3
4
- Determine the probability density function of \(X\).
Fully justify your answer.
4 - A 6 metre clothes line is connected between the point \(P\) on one building and the point \(Q\) on a second building.
Roy is concerned the clothes line may break. He uses the random variable \(X\) to model the distance in metres from \(P\) where the clothes line breaks.
4
- State a criticism of Roy's model.
4
- (ii) On the axes below, sketch the probability density function for an alternative model for the clothes line.
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