Introduction to Probability & Statistics

Statistical experiment

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

Experimental data

The data gathered from a statistical experiment.

Sample Space

Set of 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 iff they have no sample points in common.

Independent

Two events are said to be independent iff 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

A possible result of a statistical experiment.

Discrete

Outcomes that can take on only specific, distinct values. For example:

• the number of students in a class
• the result of a dice roll
• the count of defective items in a batch

Continuous

Outcomes that can take on any value within a range. For example:

• height
• weight
• time
• temperature measurements.

Observational data

Population of interest

A specific group that a researcher aims to study in order to draw meaningful conclusions or make statistical inferences about its characteristics.

Variable of interest

A changing quantity which is being measured in an experimental study.

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.