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Refer to Exercise 12.a. Find the conditional probability

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 15E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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5
Problem 15E

Refer to Exercise 12.

a. Find the conditional probability mass function PY|X(y | 3).

b. Find the conditional probability mass function pX|Y(x|1).

c. Find the conditional expectation E(Y | X = 3).

d. Find the conditional expectation E(X | Y = 1).

Step-by-Step Solution:
Step 1 of 3

Solution 15E

Step1 of 5:

We have the cost of an engine repair is $50, and the cost of a transmission repair is $100.

Let us take T it represent the total cost of repairs during a one-hour time interval.

That is

y

x

0

1

2

3

0

0.13

0.1

0.07

0.03

1

0.12

0.16

0.08

0.04

2

0.02

0.06

0.08

0.04

3

0.01

0.02

0.02

0.02

Here our goal is:

a).We need to find the conditional probability mass function  

b).We need to find the conditional probability mass function

c).We need to find the conditional expectation E(Y|X = 3).

d).We need to find the conditional expectation E(X|Y = 1).

Step2 of 5:

a).

Consider,

y

Total

x

0

1

2

3

0

0.13

0.1

0.07

0.03

0.33

1

0.12

0.16

0.08

0.04

0.4

2

0.02

0.06

0.08

0.04

0.2

3

0.01

0.02

0.02

0.02

0.07

Total

0.28

0.34

0.25

0.13

1

Where

,  

Step 2 of 3

Chapter 2.6, Problem 15E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Refer to Exercise 12.a. Find the conditional probability

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