|A 3 The continuous random variable X has probability density function given by fx(x) = c(1 - x*), -Isxs1, where c is a suitable constant. i. Show that e = % and plot the graph of fx(x) against x. ii. Show that the cumulative distribution function of X is given by x <-1 2+3x-x3 Fx(x) = -1 sxs1 4 1 x > 1 Also find P (-sxs). iii. Obtain the standard deviation of X, to 3 significant figures.

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