Mathematics S1,S2,S3 WST01: Continuous Random Variables Topical Past Paper Questions

A farmer grows watermelons on a farm. The weights, in kilograms, of the watermelons are modelled by the random variable W with probability density function $$ \mathrm{f}(w)=\left\{\begin{aligned}&\frac{1}{9}(6-w)(w-2)&\quad&2\leqslant w\leqslant5\\ &0&\quad&otherwise\end{aligned}…

The continuous random variable X has a probability density function given by $$ \begin{aligned}&\mathrm{f}(x)=\left\{\begin{aligned}\\ &\frac{2}{21}x&&0\leqslant x\leqslant k\\&\frac{2}{15}\Big(6-x\Big)&&k (2)

The continuous random variable D is uniformly distributed over the interval $ [x - 1, x + 5] $ where x is a constant. A random sample of $n$ observations of $D$ is taken, where $n$ is large. (a) Use the Central Limit Theorem to find an approximate distribution for $\overline{D}$…