STAT 301 - Business Statistics
Lecture Review #9 - Expected Value

Review questions:

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

2) What is meant by the expected variance of a random variable?

Computational exercises:

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 net return on a $1 field bet.

2) Find the variance of the net winnings, for the craps field bet described in Problem #1 above.

3) 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:

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

4) Find the variance for Disney's return, for the data in Problem #3.

SOLUTIONS:
1) -2/36 or -.0556
2) 1.16
3) -15.25%
4) 713.7