## Overview

• Statistical Inference = generating conclusions about a population from a noisy sample
• Goal = extend beyond data to population
• Statistical Inference = only formal system of inference we have
• many different modes, but two broad flavors of inference (inferential paradigms): Bayesian vs Frequencist
• Frequencist = uses long run proportion of times an event occurs independent identically distributed repetitions
• frequentist is what this class is focused on
• believes if an experiment is repeated many many times, the resultant percentage of success/something happening defines that population parameter
• Bayesian = probability estimate for a hypothesis is updated as additional evidence is acquired
• statistic = number computed from a sample of data
• statistics are used to infer information about a population
• random variable = outcome from an experiment
• deterministic processes (variance/means) produce additional random variables when applied to random variables, and they have their own distributions

## Probability

• Probability = the study of quantifying the likelihood of particular events occurring
• given a random experiment, probability = population quantity that summarizes the randomness
• not in the data at hand, but a conceptual quantity that exist in the population that we want to estimate

### General Probability Rules

• discovered by Russian mathematician Kolmogorov, also known as “Probability Calculus”
• probability = function of any set of outcomes and assigns it a number between 0 and 1
• \(0 \le P(E) \le 1\), where \(E\) = event
• probability that nothing occurs = 0 (impossible, have to roll dice to create outcome), that something occurs is 1 (certain)
• probability of outcome or event \(E\), \(P(E)\) = ratio of ways that \(E\) could occur to number of all possible outcomes or events
• probability of something = 1 - probability of the opposite occurring
• probability of the union of any two sets of outcomes that have nothing in common (mutually exclusive) = sum of respective probabilities