# Refer to Exercise 1. a. Find the conditional probability

## Problem 3E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Problem 3E

Refer to Exercise 1.

a. Find the conditional probability mass function PY|X(y|0).

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

c. Find the conditional expectation E(Y | X = 0).

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

Step-by-Step Solution:

Step 1 of 4:

The number of days on which the ozone standard is exceeded is X and

The number of days on which the particulate matter standard is exceeded is Y.

Then the joint probability mass function of X and Y is given in the table below.

 Y X 0 1 2 0 0.10 0.11 0.05 1 0.17 0.23 0.08 2 0.06 0.14 0.06

Our goal is:

a). Find the conditional probability mass function .

b). Find the conditional probability mass function .

c). Find the conditional expectation .

d). Find the conditional expectation .

a).

Now we have to find the conditional probability mass function .

We have a table.

 Y X 0 1 2 0 0.10 0.11 0.05 1 0.17 0.23 0.08 2 0.06 0.14 0.06

Then the conditional probability mass function is

and

Then, we substitute and values.

Therefore is 0.3846.

and

Then, we substitute and values.

Therefore is 0.4230.

and

Then, we substitute and values.

Therefore is 0.1923.

Hence the conditional probability mass function is

.

Step 2 of 2

##### ISBN: 9780073401331

Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9780073401331. The answer to “Refer to Exercise 1. a. Find the conditional probability mass function PY|X(y|0).________________b. Find the conditional probability mass function PX|Y(x|1).________________c. Find the conditional expectation E(Y | X = 0).________________d. Find the conditional expectation E(X | Y = 1).” is broken down into a number of easy to follow steps, and 37 words. The full step-by-step solution to problem: 3E from chapter: 2.6 was answered by Patricia, our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4th. Since the solution to 3E from 2.6 chapter was answered, more than 231 students have viewed the full step-by-step answer. This full solution covers the following key subjects: conditional, Find, expectation, Probability, mass. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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