# The joint pmf of X and Y is f (x, y) = 1/6, 0 ?x + y ? 2,

## Problem 6E Chapter 4.2

Probability and Statistical Inference | 9th Edition

• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Probability and Statistical Inference | 9th Edition

4 5 0 242 Reviews
15
1
Problem 6E

PROBLEM 6E

The joint pmf of X and Y is f (x, y) = 1/6, 0 ≤x + y ≤ 2, where x and y are nonnegative integers.

(a) Sketch the support of X and Y.

(b) Record the marginal pmfs fX(x) and fY(y) in the “margins.”

(c) Compute Cov(X,Y).

(d) Determine ρ, the correlation coefficient.

(e) Find the best-fitting line and draw it on your figure.

Step-by-Step Solution:

Step 1 of  8

a) Construct a table for a given pmf        0

 y x 0 1 2 0 1/6 1/6 1/6 3/6 1 1/6 1/6 0 2/6 2 1/6 0 0 1/6 3/6 2/6 1/6 1

Step 2 of  8

b)  Marginal pmf of x is

 x 0 1 2 Total 3/6 2/6 1/6 1

Marginal pmf of y is

 y 0 1 2 Total 3/6 2/6 1/6 1

Step 3 of  8

c) Now find the mean and variance by using the tables

E(X) =

=0(3/6)+1(2/6)+2(1/6)

=4/6

E(Y)=

=0(3/6)+1(2/6)+2(1/6)

=4/6

E(XY)=

=1(1)(⅙)

=1/6

cov(X,Y)=E(XY)-E(X)E(Y)

=1/6-4/6(4/6)

= -10/36

Step 4 of  8

d)E(X2)=

=0(3/6)+1(2/6)+4(1/6)

=1

=V(x)

=E(X2) -[ E(X)]2

=1- (4/6)2

=20/36

Step 5 of 7

Step 6 of 7

##### ISBN: 9780321923271

Since the solution to 6E from 4.2 chapter was answered, more than 257 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 6E from chapter: 4.2 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. The answer to “The joint pmf of X and Y is f (x, y) = 1/6, 0 ?x + y ? 2, where x and y are nonnegative integers.(a) Sketch the support of X and Y.(b) Record the marginal pmfs fX(x) and fY(y) in the “margins.”(c) Compute Cov(X,Y).(d) Determine ?, the correlation coefficient.(e) Find the best-fitting line and draw it on your figure.” is broken down into a number of easy to follow steps, and 60 words. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9th. This full solution covers the following key subjects: Best, coefficient, correlation, cov, determine. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271.

#### Related chapters

Unlock Textbook Solution

The joint pmf of X and Y is f (x, y) = 1/6, 0 ?x + y ? 2,

×
Get Full Access to Probability And Statistical Inference - 9th Edition - Chapter 4.2 - Problem 6e

Get Full Access to Probability And Statistical Inference - 9th Edition - Chapter 4.2 - Problem 6e

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
We're here to help