1. A company markets two products (Product A and Product B) through mail order. The company will market them in sequence with the first mail order offer for product A. It feels that there is a 30% chance that any customer will purchase product A. Product B is offered some months later. It is felt, for product B, that there is a 30% chance of selling product B to a customer if the customer purchased product A and a 5% chance of selling product B to a customer who did not purchase product A.

What is the probability of not selling product B to a particular customer?

2. A quality control department finds that it accepted only 5% of all bad items and it rejected only 1% of good items. A supplier has just delivered a shipment of a certain item. Past records show that only 90% of the parts of that supplier are good. If the department accepts an item, what is the probability that the item is bad?

Solution Preview

1. What is the probability of not selling product B to a particular customer?

P(A) = 0.30, P(A') = 1 - 0.3 = 0.7
Probability of ...

Solution Summary

This response applies the concepts of marginal and joint probability to different business scenarios.

Let X1 and X2 have the joint pmf p(x1,x2) = (x1x2)/36 x1=1,2,3 and x2=1,2,3, zero elsewhere. Find first the joint pmf of Y1=X1X2 and Y2=X2, and then find the marginal pmf of Y1.

Determine the value of c that makes the function f(x,y) = c(x+y) a jointprobability density function over the range:
x greater than 0 and less than 3 and x less than y less than x+2
a) P(X<1, Y<2)
b) P(11)
d) P(X<2, Y<2)
e) E(X)
f) V(X)
g) Marginalprobability distribution of X
h) Conditional probabilit

A fair coin is tossed four times and X is number of heads on first three tosses and Y on last three. What is the jointprobability mass function of x and y? What is the marginal pmf? Are X and Y independent?

Let X and Y have joint probability mass function Pr{X = i, Y = j}= c(i + 1)(j + 2) for
i >= 0, j >= 0, and i + j < 4. Determine
a) the marginalprobability mass function of X
b) the probability mass function of Y
c) the conditional probability mass function of X given Y = 0
d) the probability mass function of Z = X + Y

Let X, Y be independent, standard normal random variables, and let U = X + Y and V = X - Y.
(a) Find the jointprobability density function of (U, V) and specify its domain.
(b) Find the marginalprobability density function of U and V specifying the domain in each case.
(c) Explain why U and V are independent
Joint probab

I own three fuel terminals. one in the north, one in the south and one in the mid-west. My north terminal house 25% of my employees, my south terminal house 40% of my employees and my mid-west house 35% of my employees. 10% of my north employees failed a management test, 15% of my south and 5% of my mid-west.
Using excel I'm

Health Insurance (Proportion of Population)
Yes No
Age 18 to 34 750 170
35 and older 950 130
a. Develop a jointprobability table for these data and use the table to answer the remaining questions.
b. What do the mar

A metropolitan school system consists of three school districts-norths, south, central. The north district contains 25% of all students, the south district contains 40%, and the central district contains 35%. A minimum-competency test was given to all students; 10% of the north district students failed, 15% of the south distri