Brief introduction into the class: S520 is an introductory course in statistics for graduate students taught by Professor Michael Trosset. It aims for depth in each of the subjects we talk about, explaining the why’s and wherefore’s of each topic instead of trying to cram as many topics in as possible (which is a major perk, in my opinion). It’s actually taught in conjunction with S320, the undergraduate version of the same course, so I think most of the other students in the course are undergrads (not a bad thing, just an observation). You can read more about it on the pages linked above. Ok, on with the notes.
Chapter 3, Probability
- Basics of modern probability devised by Kolmogorov as discussed last time.
- Kolmogorov’s probability space has three major components
- , the sample space – the universe of possible experimental outcomes
- , the collection of subsets of called “events”- events have well-defined probabilities
- , the probability measure-a function that assigns real numbers (called “probabilities”) to events-in proper notation, that looks like:
- There are several criteria the probability measure has to satisfy, though many of the are by convention only.
- Convention – we require , where is the probability of any given event.
- If not going to happen, generally speaking. (Apparently there are exceptions I don’t know about.)
- If definitely going to happen.
- Convention – has to be an event in
- Crucial property: If and are disjoint events, then the probablility of their union is:
- Because of those conventions, we can learn these things:
are disjoint, then by “crucial property”:
- If , then
Section 3.3 Finite Sample Space
- has a finite number of outcomes, represented by
Friday – Conditional probabilities
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