Let X denote the number of times a certain numerical control machine will malfunction per a day. Let Y denote the number of times a technician is called on an emergency call per a day. Their (discontinuous) joint probability distribution is given as: Y X 2 3 4 5 1/24 1/12 1/12 3/24 1/12 1/24 1/24 3/12 1/12 1/24 1/12 1/24 1 (a) Are X and Y independent? (b) Compute P(X < 1 and Y > 4). (c) Compute P(Y < 3[X = 1). %3D

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Let X denote the number of times a certain numerical control machine will malfunction
per a day. Let Y denote the number of times a technician is called on an emergency call
per a day. Their (discontinuous) joint probability distribution is given as:
Y
X
2
3
4
5
1/24
1/12
1/12
3/24
1/12
1/24
1/24
3/12
1/12
1/24
1/12
1/24
1
(a) Are X and Y independent?
(b) Compute P(X < 1 and Y > 4).
(c) Compute P(Y < 3[X = 1).
%3D
Transcribed Image Text:Let X denote the number of times a certain numerical control machine will malfunction per a day. Let Y denote the number of times a technician is called on an emergency call per a day. Their (discontinuous) joint probability distribution is given as: Y X 2 3 4 5 1/24 1/12 1/12 3/24 1/12 1/24 1/24 3/12 1/12 1/24 1/12 1/24 1 (a) Are X and Y independent? (b) Compute P(X < 1 and Y > 4). (c) Compute P(Y < 3[X = 1). %3D
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