1. 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=1,3,5. c. List the cumulative distribution function F(x) d. List the cumulative distribution function F(y)

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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1.
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=1,3,5.
c. List the cumulative distribution function F(x)
d. List the cumulative distribution function F(y)
x
f(x,y)
2
0.05
0.05
0.05
0.10
Y
0.00
0.20
3
35
3
0.10
0.35
0.10
Transcribed Image Text:1. 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=1,3,5. c. List the cumulative distribution function F(x) d. List the cumulative distribution function F(y) x f(x,y) 2 0.05 0.05 0.05 0.10 Y 0.00 0.20 3 35 3 0.10 0.35 0.10
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