Question: Question 1 (20 points) The random variable X takes the values 0, 1, 2 and 3 according to the following probability table, X 0

Question 1 (20 points) The random variable X takes the values 0, 1, 2 and 3 according to the following probability table, X 0 1 2 3 P(X = x) a a+0.1 b b+0.2 (a) Suppose the expectation of X is 2, find the values for a and b. (b) What is the variance of this random variable? (c) Consider another independent random variable Y with the following proba- bility distribution y 0 1 P(Yy) 0.2 0.8 Find the distribution of XY. (d) Find the distribution of X + Y.

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