94 CHAPTER 3. FIRST STEP ANALYSIS FOR STOCHASTIC PROCESSES
Problems to Work for Understanding
- How many heads were obtained in your sequence of 100 flips? What
is the class average of the number of heads in 100 flips? What is the
variance of the number of heads obtained by the class members in the
number of heads? - How many flips did it take before you reached a net gain of +10 or a
net loss of−10? What is the class average of the number of flips before
reaching a net gain of +10 or a net loss of−10? - How many of the class reached a net gain of +10 before reaching a net
loss of−10? - What is the maximum net value achieved in your sequence of flips?
What is the class distribution of maximum values achieved in the se-
quence of flips?
Outside Readings and Links:
- Virtual Laboratories in Probability and Statistics Red and Black Game
- University of California, San Diego, Department of Mathematics, A.M.
Garsia A java applet that simulates how long it takes for a gambler to
go broke. You can control how much money you and the casino start
with, the house odds, and the maximum number of games. Results are
a graph and a summary table. Submitted by Matt Odell, September
8, 2003.
3.2 Ruin Probabilities
Rating
Mathematically Mature: may contain mathematics beyond calculus with
proofs.