study guide

Study guide for test 1

The test will be Thursday, February 10. It will cover the probability theory that we have studied, for homework assignments 1, 2 and 3. The test will be 12.5% of your grade (the two tests you will have together are 25% of your grade).

The test will consist of problems similar to your homework, some of which will involve the making of spreadsheets. The test will not favor one homework assignment over the others; each problem will be weighted about the same. For each assignment, please be able to do the following:

1. Be able to find the probability of events from simple probability experiments such as tossing coins or rolling dice (including 4-sided dice).

Be able to find the probability that two independent events occur (P(A and B) = P(A)P(B)). Be able to find the probability that one event or the other or both occur (P(A or B) = P(A) + P(B) - P(A and B)). The test questions will be similar to your homework problems involving dice and cards. In particular, you may be asked questions such as "In 1300 draws, how many times (on average) would you expect to draw a king?" [Answer, 100.]

You may also be asked to find the probability that each of several different events occur, or that none of several different events occur [the rocket failure problem], or at least one of several events occur [the earthquake example].

2. Be able to find the expected value of a random variable. For example, the expected loss of an insurance policy, if the probabilities of different losses are given; or the expected win or loss of a simple game, if the payoffs of different outcomes are specified.

Be able to use Excel to draw histograms or relative frequency histograms. Be able to do this for prepared spreadsheets that simulate dice or coin experiments, or for spreadsheets that give tables of data (such as home prices), or for your own spreadsheets that generate random numbers. Be able to generate random numbers in a spreadsheet, either uniformly distributed [using =RAND( )], or exponentially distributed [using =-1.0*Mean*LN(RAND( )) ].

3. Be able to generate customer arrival times according to a Poisson process.

Be able to find the mean, variation, and standard deviation of several numbers by hand.

Be able to use Excel to find mean, variation and standard deviation of a range of numbers.

Be able to use Excel to find simple probabilities involving normal distributions.

1.	Be able to find the probability of events from simple probability experiments such as tossing coins or rolling dice (including 4-sided dice).
	Be able to find the probability that two independent events occur (P(A and B) = P(A)P(B)). Be able to find the probability that one event or the other or both occur (P(A or B) = P(A) + P(B) - P(A and B)). The test questions will be similar to your homework problems involving dice and cards. In particular, you may be asked questions such as "In 1300 draws, how many times (on average) would you expect to draw a king?" [Answer, 100.]
	You may also be asked to find the probability that each of several different events occur, or that none of several different events occur [the rocket failure problem], or at least one of several events occur [the earthquake example].
2.	Be able to find the expected value of a random variable. For example, the expected loss of an insurance policy, if the probabilities of different losses are given; or the expected win or loss of a simple game, if the payoffs of different outcomes are specified.
	Be able to use Excel to draw histograms or relative frequency histograms. Be able to do this for prepared spreadsheets that simulate dice or coin experiments, or for spreadsheets that give tables of data (such as home prices), or for your own spreadsheets that generate random numbers. Be able to generate random numbers in a spreadsheet, either uniformly distributed [using =RAND( )], or exponentially distributed [using =-1.0MeanLN(RAND( )) ].
3.	Be able to generate customer arrival times according to a Poisson process.
	Be able to find the mean, variation, and standard deviation of several numbers by hand.
	Be able to use Excel to find mean, variation and standard deviation of a range of numbers.
	Be able to use Excel to find simple probabilities involving normal distributions.