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# Refer to Exercise 12.a. Find the conditional probability

ISBN: 9780073401331 38

## Solution for problem 15E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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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

Step 3 of 3

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