A bookstore at the Hartsfield-Jackson airport in Atlanta sells reading materials (paperback books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.) A point-of-sale terminal collects a variety of information about customer purchases. The accompanying table shows the number of snack items and the number of items of reading material purchased by the most recent 600 customers. Reading materials snacks 0 1 2 0 0 60 18 1 240 90 30 2 120 30 12 Using the data in the table construct an empirical discrete bivariate probability distribution for x = number of snack items and y = number of reading materials for a randomly selected customer purchase. What is the probability of a customer purchase consisting of one item of reading materials and two snack items? What is the probability of a customer purchasing one snack item only? Why is the probability f(x=0, y=0)=0?
A bookstore at the Hartsfield-Jackson airport in Atlanta sells reading materials (paperback books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.) A point-of-sale terminal collects a variety of information about customer purchases. The accompanying table shows the number of snack items and the number of items of reading material purchased by the most recent 600 customers. Reading materials snacks 0 1 2 0 0 60 18 1 240 90 30 2 120 30 12 Using the data in the table construct an empirical discrete bivariate probability distribution for x = number of snack items and y = number of reading materials for a randomly selected customer purchase. What is the probability of a customer purchase consisting of one item of reading materials and two snack items? What is the probability of a customer purchasing one snack item only? Why is the probability f(x=0, y=0)=0?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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A bookstore at the Hartsfield-Jackson airport in Atlanta sells reading materials (paperback books, newspapers, magazines) as well as snacks (peanuts, pretzels, candy, etc.) A point-of-sale terminal collects a variety of information about customer purchases. The accompanying table shows the number of snack items and the number of items of reading material purchased by the most recent 600 customers.
Reading materials | |||
snacks | 0 | 1 | 2 |
0 | 0 | 60 | 18 |
1 | 240 | 90 | 30 |
2 | 120 | 30 | 12 |
- Using the data in the table construct an empirical discrete bivariate probability distribution for x = number of snack items and y = number of reading materials for a randomly selected customer purchase. What is the probability of a customer purchase consisting of one item of reading materials and two snack items? What is the probability of a customer purchasing one snack item only? Why is the probability f(x=0, y=0)=0?
- Show the marginal probability distribution for the number of snack items purchased. Compute the expected value and variance.
- What is the expected value and variance for the number of reading materials purchased by a customer
- Show the probability distribution of t = total number of items for a randomly selected customer purchase. Compute its expected value and variance. (You are constructing a new random variable from the table. The random variable t = x + y is the number of objects purchased).
- Compute the
covariance andcorrelation coefficient between x and y. What is the relationship, if any, between the number of reading materials and number of snacks purchased? (You're back to using the distribution from a - c., and the var(x+y) from part d.)
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