2. Consider the function: ;0sxs1 c(2 - x) ; 1 < xs 2 ; otherwise. Find c to make this the PDF of a R.V. X, then plot/draw the resulting fx. Calculate and express X's CDF Fx(x), the same way fx(x) is expressed cx fx(x) = (a) (b) above, for four regions of x: ;x < 0 ;0sxs1 ;1 m) = ; In this problem X has one such m. Show that this median is the same as the mean of X. Does it always have to be (i.e., for other R.V.s)?

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