4. Let X be a random variable with c.d.f., 0, if x < 0 1 Fx (x) = • if 0sx < 1/2 2' 1, if x 2 1/2 Note Fx (x) is not continuous at 0 = x. Thus X is not a continuous variable. However, since Fx (x) is not a step function of x, X is not a discrete random variable. X is in fact a mixed random variable. (1) Draw Fx(x). (2) Find fx (x). (3) Find P(0 < X < 4).

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