Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given below: a. Find the marginal distribution g(x), x = 1, 2, 3. b. Find the marginal distribution h(y), y = 1, 2, 3. c. List the cumulative distribution function F(x). d. List the cumulative distribution function F(y). e. Find the conditional distribution of f(xly), P(X= 11Y = 3). f. Find the conditional distribution of f (ylx), P(X=31 Y = 3). g. Determine if the random variables are statistically independent considering f (2, 1). x f(x,y) 1 2 3 1 0.05 0.05 0.10 3 0.05 0.10 0.35 Y 5 0.00 0.20 0.10

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