Probability Models

Question 1

Why do we study probability?

Answer 1

Many statistical application (sampling, randomization, inference) are based on understanding how ‘likely’ events are.

Question 2

Probability

Answer 2

The chance or likelihood of some event occuring.

Relative frequency (‘frequentist’) approximation:
proportion of times the outcome would occur in a long  series of repetitions

P(x) = # times X occurs/ # times procedure was repeated

Question 3

Probability Model

Answer 3

A mathematical description (equation, graph, table) of an ‘experiment’ that identifies all possible outcomes and their associated probabilities.

Normal; Binomial; Uniform; Poisson

Question 4

Experiment

Answer 4

The procedure we’re doing that has a random outcome.

Question 5

Sample Space (Continous/Discrete)

Answer 5

Collection of all possible outcomes for an experiment.

Continous: specifies the interval (of infinite) values over which the outcomes occur.

Discrete: countble number of outcomes

Question 6

Event (Simple/Compound)

Answer 6

A group of outcomes that share a feature of interest; a subset of the sample space.

Simple: Can only happen one way.

Compound: can happen in multiple ways (contain more than one outcome)

Question 7

Mutually Exclusive

Answer 7

Events have no shared outcomes. We can add their probabilities together.

Question 8

Independent

Answer 8

Events occurring in tandem whose probabilities are not influenced by each other.

We can multiply their probabilities.