RANDOM VARIABLESSHORT REVIEW

CS6140

Predrag RadivojacKHOURY COLLEGE OF COMPUTER SCIENCES

NORTHEASTERN UNIVERSITY

Spring 2021

RANDOM VARIABLES

Age: 35 Likes sports: YesHeight: 1.85m Smokes: NoWeight: 75kg Marital status: SingleIQ: 104 Occupation: Musician

A/Dconverter 1

1

1

0

000

01

1

0 1

Age: 26 Likes sports: YesHeight: 1.75m Smokes: NoWeight: 79kg Marital status: DivorcedIQ: 103 Occupation: Athlete

Analog Digital

1

Pictures from the Internet.

Picture from the Internet.

EXAMPLE: RANDOM VARIABLES

Picture from the Internet.

EXAMPLE: RANDOM VARIABLES

RANDOM VARIABLE: FORMAL DEFINITION

DISCRETE RANDOM VARIABLE

EXERCISE: QUANTIZATION

CONTINUOUS RANDOM VARIABLE

CONTINUOUS RANDOM VARIABLE

JOINT AND MARGINAL DISTRIBUTIONS

EXERCISE: JOINT DISTRIBUTIONS

Picture from the Internet.

JOINT AND MARGINAL DISTRIBUTIONS

CONDITIONAL DISTRIBUTIONS

CHAIN RULE

INDEPENDENCE OF RANDOM VARIABLES

EXPECTATIONS

WELL-KNOWN EXPECTATIONS

CONDITIONAL EXPECTATIONS

EXERCISE: EXPECTATIONS

Picture from the Internet.

EXPECTATIONS FOR TWO VARIABLES

WELL-KNOWN EXPECTATIONS

MIXTURES OF DISTRIBUTIONS

MIXTURES OF GAUSSIANS

GRAPHICAL REPRESENTATIONS

GRAPHICAL REPRESENTATIONS

GRAPHICAL REPRESENTATIONS