×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide

Refer to Exercise 31. Assume the first card is not

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 32SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

4 5 1 275 Reviews
19
1
Problem 32SE

Refer to Exercise 31. Assume the first card is not replaced before the second card is drawn.

a. Find the joint probability mass function of X and Y.

b. Find the marginal probability mass functions pX(x) and pY(y).

c. Find μx and μy.

d. Find μXY.

e. Find Cov(X, Y).

Step-by-Step Solution:

Answer

 

Step 1 of 5</p>

a) For constructing joint probability mass function

   First we need to write the range of X and y

   Here X represents the number on the first card  

   Then X=1,2,3

   Here Y represents the number on the first card  

   Then Y=1,2,3

   

  The first card is not replaced before second card is drawn

 So the probability of getting the same card is 0

   The remaining possibilities are (1,2),(1,3),(2,1),(2,3),(3,1),(3,2)

   The number of outcomes are 6

   

  Each outcome having the equal probability=⅙

Now we are constructing the joint probability mass function

Y\ X

1

2

3

1

0

1/6

1/6

1/3

2

1/6

0

1/6

1/3

3

1/6

1/6

0

1/3

1/3

1/3

1/3

1

Step 2 of 5</p>

b) The marginal probability mass function of X is

     

X

1

2

3

Total

1/3

1/3

1/3

1

The marginal probability mass function of Y is

     

Y

1

2

3

Total

1/3

1/3

1/3

1

Step 3 of 5</p>

c) Mean(=E(X)

                     =

                     = 1(⅓)+2(⅓)+3(⅓)

                     = 2

     Mean(=E(Y)

                     =

                     = 1(⅓)+2(⅓)+3(⅓)

                     = 2

Step 4 of 5

Chapter 2, Problem 32SE is Solved
Step 5 of 5

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Refer to Exercise 31. Assume the first card is not

×
Log in to StudySoup
Get Full Access to Statistics - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Statistics - Textbook Survival Guide
×
Reset your password