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1. Let X be a discrete random variable with the probability mass function P(x) = kx2...

1. Let X be a discrete random variable with the probability mass function P(x) = kx2 for x = 2, 3, 4, 6.

(a) Find the appropriate value of k.

(b) Find P(3), F(3), P(4.2), and F(4.2).

(c) Sketch the graphs of the pmf P(x) and of the cdf F(x).

(d) Find the mean µ and the variance σ 2 of X. [Note: For a random variable, by definition its mean is the same as its expectation, µ = E(X).]

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