Introduction to Probability & Statistics

A statistical experiment is a process designed and conducted to obtain data under a controlled and uncontrolled background. The outcome depends purely on chance.

Experimental data

The data gathered from a statistical experiment.

Sample Space

Set of elements that represent all possible outcomes of a statistical experiment. Denoted by .

Sample Point

An element of the sample space.

Event

A subset of the sample space.

Mutually Exclusive

Two events are said to be mutually exclusive if they have no sample points in common.

Independent

Two events are said to be independent when the occurence of one does not affect the probability of the occurence of the other.

Complement

Complement of the event (of ) is denoted by . An event consisting of all the sample points that are in and not .

Union

Union of two or more events, is the event containing all sample points that belong to any one of the events.

Intersection

Intersection of two or more events, is the event containing all sample points that belong to all of the events.

Outcome

2 types.

• Discrete
• Continuous

Observational data

Census

The process of gathering information about the members of a given population of interest.

Cohort

A group of subjects who share a particular event during a particular time duration.