# Question

The random variable x takes on the values 1, 2, or 3 with probabilities (1 + 3k)/3, (1 + 2k)/3, and (0.5 + 5k)/3, respectively.

(a) Find the appropriate value of k.

(b) Find the mean and variance of x.

(c) Find the cumulative distribution function.

(a) Find the appropriate value of k.

(b) Find the mean and variance of x.

(c) Find the cumulative distribution function.

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