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# Refer to Exercise 9.a. Find the conditional probability

ISBN: 9780073401331 38

## Solution for problem 11E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 11E

Refer to Exercise 9.

a. Find the conditional probability mass function pY|X(y|4).

b. Find the conditional probability mass function pX|Y(x|3).

c. Find the conditional expectation E(Y | X = 4).

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

Step-by-Step Solution:

Step 1 of 4:

Bolt manufactured for a certain for a certain purpose classified as acceptable,downgraded or scrap. In a  lot of 500 bolts, if X denote the number of downgraded bolts, Y dente the number of scraps. The joint probability mass function of X and Y is given . here we can find the marginal probability function by adding the rows and columns.

 Y X 0 1 2 3 4 0 0.06 0.03 0.01 0 0 0.1 1 0.06 0.08 0.04 0.02 0 0.2 2 0.04 0.05 0.12 0.06 0.03 0.3 3 0 0.03 0.07 0.09 0.06 0.25 4 0 0 0.02 0.06 0.07 0.15 0.16 0.19 0.26 0.23 0.16

.

We have to find

The conditional probability mass function PY/X(y/4). The conditional probability mass function PX/Y(x/3). The conditional expectation E (Y/X=4). The conditional expectation E (X/Y=3).

Step 2 of 4:

The conditional probability mass function PY/X(y/4) have to find for different values of y. By using the table,

(i)   PY/X(0/4) =

=

=   0

(ii)  PY/X(1/4)  =

=

=    0

(iii)  PY/X(2/4) =

=

=

(iv)  PY/X(3/4)  =

=

=

(v) PY/X(4/4)    =

=

=

Step 3 of 3

##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 11E from chapter: 2.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: conditional, Find, expectation, Probability, mass. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “Refer to Exercise 9.a. Find the conditional probability mass function pY|X(y|4).________________b. Find the conditional probability mass function pX|Y(x|3).________________c. Find the conditional expectation E(Y | X = 4).________________d. Find the conditional expectation E(X | Y = 3).” is broken down into a number of easy to follow steps, and 36 words. Since the solution to 11E from 2.6 chapter was answered, more than 305 students have viewed the full step-by-step answer.

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Refer to Exercise 9.a. Find the conditional probability

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