3. A cumulative distribution function of a discrete random variable X is given as %3D 1s x< 2 F (x) = { 8 2s x< 3 k+5 3s x< 4 %3D 5k X24 10 where k is a constant. (a) Show thatk 2. (b) Find the median of the distribution. (c) Use F) to calculate P(2 s X < 4). (d) Find the probability distribution function of X. (e) Determine the mean and variance of X. 0k一8

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