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# Refer to Exercise 4.a. Find the conditional probability ISBN: 9780073401331 38

## Solution for problem 6E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Problem 6E

Refer to Exercise 4.

a. Find the conditional probability mass function PY|X(y|1).

b. Find the conditional probability mass function PX|Y(x|2).

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

d. Find the conditional expectation E(X | Y = 2).

REFERENCE EXERCISE 4: In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below: a. Find the marginal probability mass function of X.

b. Find the marginal probability mass function of Y.

c. Are X and Y independent? Explain.

d. Find μX and μY.

e. Find σX and σY.

f. Find Cov(X, Y).

g. Find ρ(X, Y).

Step-by-Step Solution:

Step 1 of 5:

Here,it is given that X be the number with too little clearance and Y be the number with too much clearance.

Also the joint probability mass function of X and Y is given as

 Y X 0 1 2 3 0 0.15 0.12 0.11 0.10 1 0.09 0.07 0.05 0.04 2 0.06 0.05 0.04 0.02 3 0.04 0.03 0.02 0.01

Using these,we have to find the required probabilities and expectations.

Step 2 of 5

Step 3 of 5

##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 6E from chapter: 2.6 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 6E from 2.6 chapter was answered, more than 801 students have viewed the full step-by-step answer. The answer to “Refer to Exercise 4.a. Find the conditional probability mass function PY|X(y|1).b. Find the conditional probability mass function PX|Y(x|2).c. Find the conditional expectation E(Y | X = 1).d. Find the conditional expectation E(X | Y = 2).REFERENCE EXERCISE 4: In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below: a. Find the marginal probability mass function of X.b. Find the marginal probability mass function of Y.c. Are X and Y independent? Explain.d. Find ?X and ?Y.e. Find ?X and ?Y.f. Find Cov(X, Y).g. Find ?(X, Y).” is broken down into a number of easy to follow steps, and 133 words. 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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Refer to Exercise 4.a. Find the conditional probability