4. (20 points) Let X be a discrete random variable. Suppose that X has the following probability distribution: f(3) = 0.

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4 20 Points Let X Be A Discrete Random Variable Suppose That X Has The Following Probability Distribution F 3 0 1 (41.2 KiB) Viewed 22 times

4. (20 points) Let X be a discrete random variable. Suppose that X has the following probability distribution: f(3) = 0.3 if m=0 0.1 ifr=1 0.4 if = 2 if x=3 0 otherwise (a) (2 points) Find the constant k. (b) (4 points) Find the probabilities P(X<2) and P(1 < X <3) (c) (3 points) Compute the expectation (mean) of X. (d) (3 points) Compute the expectation of g(x) = x2 +1. (e) (4 points) Compute the variance of X. () (4 points) Find the cumulative distribution function F(X) of X.