# Random variables

1. Feb 20, 2005

### mutzy188

Hi I need some help. I don't think I did any of this right.

A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a$25 service charge for each repair needed. The company's research suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1% three times, and none required more than three repairs.

1. Find the expected number of repairs this kind of computer is expected to need each year.

100(.86) + 125(.09) + 150(.04) + 175(.01) = 105

2. Find the standard deviation of the number of repairs each year.

.86(100-105)^2 + .09(125-105)^2 + .04(150-105)^2 + .01(175-105)^2 = 187.5
sqrt(187.5) = 13.69

3. What are the mean and standard deviation of the company's annual expense for the service contract?
I have no clue how to do this one.

4. How many times should the company expect to have to get this computer repaired over the three-year term of lease?
None?

5. What is the standard deviation of the number of repairs that may be required during the three-year lease period?
105*3 = 315

Thanks

2. Feb 21, 2005

### Galileo

An answer like 105 should tell you something is wrong.
Use the right information: A computer needs no repairs with a probability of 86%. 1 repair with a prob. of 9%, 2 repairs with 4% and three with 1%.
Find the expectation $P(X)$ from this.

1. Find the expectation of the number of repairs squared: $P(X^2)$.
Then use: $\sigma_X^2=P(X^2)-P(X)^2$

3. Feb 21, 2005

### xanthym

HINTS GIVEN ABOVE IN RED.
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Last edited: Feb 21, 2005