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 materialssnacks0120060181240903021203012 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 customerShow 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 and correlation 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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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.CR: Chapter 7 Review

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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 and correlation 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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