0 0.08 0.08 0.13 0.05 0.04 0.00 0.00 0.03 0.01 0.06 The difference between the number of customers in line at the express checkout and the number in line at the superexpress checkout is X₂-X. Calculate the expected difference. 2 3 1 0.06 2 0.04 0.05 0.10 0.04 0.05 0.00 0.05 0.06 0.07
0 0.08 0.08 0.13 0.05 0.04 0.00 0.00 0.03 0.01 0.06 The difference between the number of customers in line at the express checkout and the number in line at the superexpress checkout is X₂-X. Calculate the expected difference. 2 3 1 0.06 2 0.04 0.05 0.10 0.04 0.05 0.00 0.05 0.06 0.07
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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### Calculating Expected Difference in Check-Out Line Customers
A certain market has both an express checkout line and a super-express checkout line. Let \( X_1 \) denote the number of customers in line at the express checkout at a particular time of day, and let \( X_2 \) denote the number of customers in line at the super-express checkout at the same time. Suppose the joint probability mass function (pmf) of \( X_1 \) and \( X_2 \) is given in the accompanying table.
| \(X_1 \backslash X_2\) | 0 | 1 | 2 | 3 |
|:----------------------:|:------:|:------:|:------:|:------:|
| 0 | 0.08 | 0.06 | 0.04 | 0.00 |
| 1 | 0.08 | 0.13 | 0.05 | 0.05 |
| 2 | 0.05 | 0.04 | 0.10 | 0.06 |
| 3 | 0.04 | 0.03 | 0.06 | 0.07 |
| 4 | 0.00 | 0.01 | 0.05 | 0.06 |
#### Explanation of the Table
The rows in the table represent the values of \( X_1 \) (number of customers in the express checkout line), while the columns represent the values of \( X_2 \) (number of customers in the super-express checkout line). Each cell in the table contains the joint probability \( P(X_1 = x_1, X_2 = x_2) \).
To calculate the expected difference between the number of customers in line at the express checkout and the number in line at the super-express checkout, we define \( D = X_1 - X_2 \). We then compute the expected value \( E(D) \) using the joint pmf.
#### Calculation Steps
1. Compute the expectations \( E(X_1) \) and
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