- (a) Explain the difference between a discrete and a continuous variable.
A random number generator on a calculator generates numbers, \(X\), to 3 decimal places, in the range 0 to 1 , e.g. 0.386 . The variable \(X\) may be modelled by a continuous uniform distribution, having the probability density function \(\mathrm { f } ( x )\), where
$$\begin{array} { l l }
\mathrm { f } ( x ) = 1 & 0 < x < 1
\mathrm { f } ( x ) = 0 & \text { otherwise }
\end{array}$$
(b) Explain why this model is not totally accurate.
(c) Sketch the cumulative distribution function of \(X\).