Dr. John Rasp's Statistics Website

Review questions:

1) What is meant by the expected value of a random variable?

Computational exercises:

NOTE that this is a continuation of the previous lecture review assignment.

1) In craps, the bettor can make what is called a "field bet." The bet is lost if a 5, 6, 7, or 8 comes up on the next roll of a pair of dice. Any other number is a win. A \$1 field bet gains \$1 if a 3, 4, 9, 10, or 11 is rolled, and gains \$2 if a 2 or 12 is rolled. The bet superficially looks appealing, because seven numbers favor the bettor while only four favor the house. Nevertheless, it is a losing proposition for the bettor (of course). Find the expected variance for the net return on a \$1 field bet.

2) It is generally not possible to predict a stock's return in advance. One technique that is sometimes used is for the analyst to envision a few plausible future "states of nature" and to estimate probabilities of occurrence and average return associated with each case. For example, one might envision future prospects for Disney for the coming year as follows:

 Economic conditions("states of nature") Estimatedprobability Estimatedreturn Depression 1% -80% Recession 60% -30% Stagnant economy 25% -5% Economic recovery 12% +20% Economic boom 2% +120%

Using these data, estimate the expected variance for Disney's return for the coming year.

SOLUTIONS:
1) [(-1)2(20/36)+(1)2(14/36)+(2)2(2/36)] - [(-2/36)2] = 1.16
2) [(-80%)2(.01) + … + (120%)2(.02)] - [(15.25%)2] = 713.7