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# Refer to Exercise 31. Assume the first card is not ISBN: 9780073401331 38

## Solution for problem 32SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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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:

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

Step 5 of 5

##### ISBN: 9780073401331

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