# Here are two random variables that are uncorrelated but ## Problem 22E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Problem 22E

Here are two random variables that are uncorrelated but not independent. Let X and Y have the following joint probability mass function:

 x y p(x, y) -1 1 1/3 0 0 1/3 1 1 1/3

a. Use the definition of independence on page 141 to show that X and Y are not independent (in fact Y = |X |, so Y is actually a function of X).

b. Show that X and Y are uncorrelated.

Step-by-Step Solution:

Step 1 of 3:

Given, let X and Y have the joint probability mass function.

 x y p(x,y) -1 1 1/3 0 0 1/3 1 1 1/3

Step 2 of 3:

The claim is to show that X and Y are not independent

If X and Y are independent

Then, P(X = 1 and Y = 1 ) = P(X =1) P(Y=1)

From the above table we have

P(X = 1 and Y = 1 ) = ⅓, P(X = 1 ) = ⅓ and P( Y = 1) = ⅔

Then, P(X =1) P(Y=1) = (⅓) (⅔)

= 2/9

Therefore, P(X = 1 and Y = 1 ) P(X =1) P(Y=1)

Hence, X and Y are not independent.

Step 3 of 3

##### ISBN: 9780073401331

Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9780073401331. The answer to “Here are two random variables that are uncorrelated but not independent. Let X and Y have the following joint probability mass function:xyp(x, y)-111/3001/3111/3a. Use the definition of independence on page 141 to show that X and Y are not independent (in fact Y = |X |, so Y is actually a function of X).________________b. Show that X and Y are uncorrelated.” is broken down into a number of easy to follow steps, and 61 words. The full step-by-step solution to problem: 22E from chapter: 2.6 was answered by Patricia, our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 22E from 2.6 chapter was answered, more than 239 students have viewed the full step-by-step answer. This full solution covers the following key subjects: function, uncorrelated, show, independent, let. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4th.

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