Statistical Inference Definitions

Sample space

All possible outcomes of an experiment

Events

Subsets of the sample space

Probability distribution (Pr)

Assigns numbers between 0 and 1 to events with pr(omega) = 1

Definition 1.1 (complement intersection and union)

Definition 1.2 (addition rule) (inclusion-exclusion)

Definition 1.3 (mutually exclusive, exhaustive events, and partitions)

Definition 1.4 (conditional probability)

Definition 1.5 (independence)

Definition 1.6 (Marginal Distribution)

Definition 1.7 (Conditional Densities)

Definition 1.8 (Independence)

Definition 1.9 (Expected Value)

Definition 1.10 (expectation of g(X))

Definition 1.11 (Expectation (Bivariate))

Definition 1.12 (Moments)

Definition 1.13 (Variance)

Definition 1.14 (Standard Deviation)

Definition 1.15 (Covariance)

Definition 1.16 (correlation)

What is univariate data and give an example

univariate data: is a single measurement per observational unit. Eg the height of each student in a class.

Continuous data:

Can take any real value in an interval.

e.g. height, weight , reaction times .

Models: Normal, Exponential, Uniform.

Discrete numeric:

Counts, usually non negative integers.

E.g. number of accidents in a week, number of goals in a football match.

Models: Binomial, Poisson, Geometric.

Nominal data:

Category’s with no natural order.

E.g hair colour, brand of cereal, country of birth.

Ordinal data

Categories with a natural order, but not numerical spacing.

E.g. customer service satisfaction rating. (“Poor”, “fair”, “good”, “excellent”)