Question: A random variable X has the cumulative distribution function F(x) = 0 for x < 1 x2 2x + 1 for 1 x < 2

A random variable X has the cumulative distribution function F(x) = 0 for x < 1 x2 2x + 1 for 1 x < 2 1 for x 2. (a) (5 points) Plot the PMF. (b) (5 points) Calculate the pdf. (c) (5 points) Calculate the mean of X. (d) (5 points) Calculate the variance of X.

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