1. ASV Chapters 1 - Sample Spaces and Probabilities
2 - Conditional Probability and Independence
3 - Random Variables
4 - Approximations of the Binomial Distribution
5 - Transforms and Transformations
6 - Joint Distribution of Random Variables
7 - Sums and Symmetry
8 - Expectation and Variance in the Multivariate Setting
10 - Conditional Distribution
11 - Appendix A, B, C, D, E, F

3. PROBABILITY IN A NUTSHELL

4. “Probability Theory” makes theoretical predictions of the occurrence of events where randomness is present, via known mathematical models.

5. “Probability Theory” makes theoretical predictions of the occurrence of events where randomness is present, via known mathematical models.

6. “Probability Theory” makes theoretical predictions of the occurrence of events where randomness is present, via known mathematical models.

7. POPULATION (of “units”)
uniform
X = “Random Variable”
symmetric unimodal
“REAL WORLD” SYSTEM
skew (positive)
PROBABILTY MODEL
YES
Model has to be tweaked.
THEORY
EXPERIMENT
Is there a significant difference?
Random Sample
Model Predictions
STATISTICS
How do we test them? NO
Model may be adequate / useful.