RANDOM V ARIABLES SHORT REVIEW CS6140 Predrag Radivojac KHOURY COLLEGE OF COMPUTER SCIENCES NORTHEASTERN UNIVERSITY Spring 2021
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