3.49 Let X denote the number of times a certain nu- merical 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 as f(x, y) 2 0.05 3 0.10 0.05 0.05 0.00 0.10 0.35 0.10 0.20 (a) Evaluate the marginal distribution of X. (b) Evaluate the marginal distribution of Y. (c) Find P(Y = 31X = 2), 135

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3.49 Let X denote the number of times a certain nu-
merical 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 as
f(x, y)
1
1
0.05
3
0.10
0.05
0.05
0.10
0.35
0.00
0.20
0.10
(a) Evaluate the marginal distribution of X.
(b) Evaluate the marginal distribution of Y.
(c) Find P(Y = 3 | X = 2).
35
Transcribed Image Text:3.49 Let X denote the number of times a certain nu- merical 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 as f(x, y) 1 1 0.05 3 0.10 0.05 0.05 0.10 0.35 0.00 0.20 0.10 (a) Evaluate the marginal distribution of X. (b) Evaluate the marginal distribution of Y. (c) Find P(Y = 3 | X = 2). 35
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