1. Section 7.2.1 Means and Variances of Random Variables
AP Statistics

2. Random Variables: Mean
AP Statistics, Section 7.2, Part 1

3. Random Variables: Example
The Michigan Daily Game you pick a 3 digit number and win $500 if your number matches the number drawn.
What is the average winnings?
AP Statistics, Section 7.2, Part 1

4. Random Variables: Example
The Michigan Daily Game you pick a 3 digit number and win $500 if your number matches the number drawn.
What is the average PROFIT?
Mean = Expected Value
AP Statistics, Section 7.2, Part 1

5. Random Variables: Variance
AP Statistics, Section 7.2, Part 1

6. Random Variables: Example
The Michigan Daily Game you pick a 3 digit number and win $500 if your number matches the number drawn.
What is the average winnings?
AP Statistics, Section 7.2, Part 1

7. AP Statistics, Section 7.2, Part 1
Law of Large Numbers
Draw independent observations at random from any population with finite mean μ.
Decide how accurately you would like to estimate μ.
As the number of observations drawn increases, the mean x-bar of the observed values eventually approaches the mean μ of the population as closely as you specified and then stays that close.
AP Statistics, Section 7.2, Part 1

8. AP Statistics, Section 7.2, Part 1
Example
The distribution of the heights of all young women is close to the normal distribution with mean 64.5 inches and standard deviation 2.5 inches.
What happens if you make larger and larger samples…
AP Statistics, Section 7.2, Part 1

9. AP Statistics, Section 7.2, Part 1

10. AP Statistics, Section 7.2, Part 1
Law of Small Numbers
Most people incorrectly believe in the law of small numbers.
“Runs” of numbers, etc.
AP Statistics, Section 7.2, Part 1

11. AP Statistics, Section 7.2, Part 1
Assignment
Exercises: odd x21
AP Statistics, Section 7.2, Part 1