DS280 - Intro to Statistics

Lecture Review #27 - Variance

This assignment continues the same problem scenarios as the previous lecture review.

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 variance of 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:

Using these data, estimate Disney's variance on its 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