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: f(x,y) 3 0.10 0.05 0.02 0.10 0.35 0.05 3 0.03 0.10 0.20 I 2 23 y 2 e. Find the conditional distribution of f(xly), P(X = 1 | Y = 1). f. Find the conditional distribution of f(xy), P(X=1|Y=2). g. Find the conditional distribution of f(xly), P(X= 1 | Y = 3).

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