1. Law of Averages (Dr. Monticino)
Law of Averages (Dr. Monticino)

2. Assignment Sheet Read Chapter 16 Assignment #9 (Due April 6th)
Read Chapter 16
Assignment #9 (Due April 6th)
Chapter 16
Exercise Set A: 1,2,3,4,5, 6,8
Exercise Set B: 1-7
Exercise C: 1,2
Review Exercises: 1-8,10

3. Overview Law of Averages Sum of Draws Box Models
Law of Averages
Absolute and relative error
Sum of Draws
Box Models
Roulette example
Texas lottery

4. Law of Averages
The law of averages says that if a chance process is repeated a large number of times , then the percentage of times that a particular event occurs is likely to be close to the probability of that event
Provided repetitions of the processes are essentially identical and independent of one another

5. Law of Averages
If the experiment is repeated N times and the probability on each repetition that an event A occurs is p, then
(#times A occurs)/N gets close to p as N gets large
Note, that this not the same as saying (#times A occurs) gets close to being exactly p*N

6. Examples
A coin is tossed repeatedly. You win $100 if exactly half the tosses are heads. Which is better:
2 tosses or 10 tosses
10 tosses or 100 tosses
Now you win $100 if the percentage of heads is between 40% and 60%. Which is better:

7. Examples Suppose you play roulette in Nevada. Which is a better:
Suppose you play roulette in Nevada. Which is a better:
Spin 50 times and win $1000 if get 40 or more reds
Spin 100 times and win $1000 if get 80 or more reds

8. Sum of Draws
For a random process producing real number values, we are often interested in the sum of the numbers produced
For example, if gambling, then your net winnings/losses is an important quantity

9. Box Models
A box model is a useful way to represent a complicated chance process
Address the following when constructing a box model
Which numbers go into the box
How many of each number
How many draws are being made from the box

10. Examples
Construct a box model for playing “red-or-black” 10 times at a Nevada roulette table, making $1 stakes
Construct a box model for betting on “17” twenty times at a Nevada roulette table, making $1 stakes
Construct a box model for buying a ticket in the Texas lottery
(Dr. Monticino)