Standard applied PDF calculations

Questions that present a real-world context with a given PDF and ask for standard probability calculations, mean, variance, or quantiles without requiring interpretation of parameters in context.

1 questions

CAIE S2 2002 June Q7
7 A factory is supplied with grain at the beginning of each week. The weekly demand, \(X\) thousand tonnes, for grain from this factory is a continuous random variable having the probability density function given by $$f ( x ) = \begin{cases} 2 ( 1 - x ) & 0 \leqslant x \leqslant 1
0 & \text { otherwise } \end{cases}$$ Find
  1. the mean value of \(X\),
  2. the variance of \(X\),
  3. the quantity of grain in tonnes that the factory should have in stock at the beginning of a week, in order to be \(98 \%\) certain that the demand in that week will be met.