S2 January 2011 Q5

EdexcelOld spec13 marksContinuous Random Variables

5. A continuous random variable \(X\) has the probability density function \(\mathrm{f}(x)\) shown in Figure 1.

Figure 1: graph of f(x), a straight line from (0, 4) down to (0.5, 0)
Figure 1
(a) Show that \(\mathrm{f}(x) = 4 - 8x\) for \(0 \leqslant x \leqslant 0.5\) and specify \(\mathrm{f}(x)\) for all real values of \(x\). (4)
(b) Find the cumulative distribution function \(\mathrm{F}(x)\). (4)
(c) Find the median of \(X\). (3)
(d) Write down the mode of \(X\). (1)
(e) State, with a reason, the skewness of \(X\). (1)
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