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

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.

Distribution
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