📗 -> 9/26/24: Course Introduction

[Lecture Slide Link]

🎤 Vocab

Sample Space: Denoted , is a set of all possible outcomes of an experiment

Sample space of rolling a dice:
Finite Sample Space: A finite amount of results can occur.
Dice rolls
Coin flips
A grades in a class
Infinitely Countable: Mappable onto the natural numbers
Number of trials until an uncertain outcome is reached (
- Rolling dice until 6 comes up
  Infinite Non-Countable: Mappable onto the real numbers
Exact distance (can be irrational for instance)
Location, speed, time, weight
Event: A subset of the sample space
If is number rolled:
Rolling a 2 is an event
Rolling an even number is an event
Rolling a number 1-6 (the entire set) is an event

A general introduction to the role of probability and statistical inference

Combinatorics and general probability
Confidence Intervals
Hypothesis Testing
Markov Chains
Maybe more ML stuff
Will NOT be covering deterministic events, only covering events with uncertainty

There is no right or wrong sample space
Flipping 2 coins can have multiple valid sample spaces
- where S is the ordering of rolls
- , where S is the # of heads
Can have finite, countably infinite, and uncountably infinite sample spaces as well