# Expected Value

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• Feb 19th 2010, 01:53 PM
tootiebee
Expected Value
No idea where to start.

The owner of a small firm has just purchased a personal computer, which she expects will serve her for the next two years. The owner has been told that she "must" buy a surge suppressor to provide protection for her new hardware against possible surges or variations in the electrical current, which have the capacity to damage the computer. The amount of damage to the computer depends on the strength of the surge. It has been estimated that there is a 2% chance of incurring 450 dollars damage, 6% chance of incurring 150 dollars damage, and 11% chance of 100 dollars damage. An inexpensive suppressor, which would provide protection for only one surge, can be purchased. How much should the owner be willing to pay if she makes decisions on the basis of expected value?
• Feb 19th 2010, 02:00 PM
vince
Quote:

Originally Posted by tootiebee
No idea where to start.

The owner of a small firm has just purchased a personal computer, which she expects will serve her for the next two years. The owner has been told that she "must" buy a surge suppressor to provide protection for her new hardware against possible surges or variations in the electrical current, which have the capacity to damage the computer. The amount of damage to the computer depends on the strength of the surge. It has been estimated that there is a 2% chance of incurring 450 dollars damage, 6% chance of incurring 150 dollars damage, and 11% chance of 100 dollars damage. An inexpensive suppressor, which would provide protection for only one surge, can be purchased. How much should the owner be willing to pay if she makes decisions on the basis of expected value?

it is always good to define what random variable you want to compute hte xpected value for. In this case, youre interested in the expected value of the random variable X, which is the amount of \$ spent on repairing the computer from surges. With the given info, we can compute
$
E[X] = .02*450+.06*150+.11*100+(1-.02-.06-.11)*0$

Since the owner would only want protection against surges if that protection cost less than the amount she would pay on average to repair the computer from surges, she would be willing to pay E[X].
• Feb 19th 2010, 02:04 PM
tootiebee
Expected Value #2
To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?
X01234P(X)0.0840.2240.3130.1960.183

Expected value =

A previous analysis of historical records found that the mean value of orders for promotional goods is 23 dollars, with the company earning a gross profit of 28% on each order. Calculate the expected value of the profit contribution next year.
Expected value =

The fixed cost of conducting the four promotions is estimated to be 10000 dollars with a variable cost of 5.25 dollars per customer for mailing and handling costs. What is the minimum number of customers required by the company in order to cover the cost of promotions? (Round your answer up to the next highest integer.) Break even point =