ASV Chapters 1 - Sample Spaces and Probabilities

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Presentation transcript:

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

PROBABILITY IN A NUTSHELL

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

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

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

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.