HKN ECE 313 FINAL EXAM REVIEW SESSION Corey

TOPICS, TOPICS • Discrete and Continuous Random Variables • Discrete Distributions • Continuous Distributions

DISCRETE AND CONTINUOUS RANDOM VARIABLES • •

DISCRETE DISTRIBUTIONS Name PMF Mean Variance Miscelleneous N/A Purpose Single trial of event with

CONTINUOUS DISTRIBUTIONS Name PDF Mean Variance Miscelleneous Purpose Describes most of the known universe.

CONDITIONAL PROBABILITY, INDEPENDENCE, TOTAL PROBABILITY, BAYES’ RULE •

JOINT CDF, PMF, AND PDF CONTINUOUS RANDOM VARIABLES DISCRETE RANDOM VARIABLES • •

JOINT PDFS OF FUNCTIONS OF RANDOM VARIABLES •

LAW OF LARGE NUMBERS AND CENTRAL LIMIT THEOREM •

Slides: 28

Download presentation

HKN ECE 313 FINAL EXAM REVIEW SESSION Corey Snyder

TOPICS, TOPICS • Discrete and Continuous Random Variables • Discrete Distributions • Continuous Distributions • Conditional Probability, Bayes’ Rule, Total Probability, Independence • Maximum Likelihood Parameter Estimation • Binary Hypothesis Testing • Markov and Chebyshev’s Inequalities • Functions of Random Variables • Joint Random Variables • Joint PDFs of Functions of Random Variables • Correlation and Covariance • Minimum Mean Square Error Estimation • Unconstrained • Linear • Law of Large Numbers and Central Limit Theorem • Bivariate Gaussian Distribution

DISCRETE AND CONTINUOUS RANDOM VARIABLES • •

DISCRETE DISTRIBUTIONS Name PMF Mean Variance Miscelleneous N/A Purpose Single trial of event with two possible outcomes. Success is a “ 1”, failure is a “ 0”. N/A Number of independent Bernoulli random variable trials until first success. N/A

CONTINUOUS DISTRIBUTIONS Name PDF Mean Variance Miscelleneous Purpose Describes most of the known universe. Memoryless Property N/A Arrivals of the Poisson Process are independent and identically distributed exponential random variables. Disjoint intervals of the Poisson Process are independent. Continuous limit of Geometric random variable; time until one arrival/success/failure. Describes random variable with equal probability for all possible outcomes.

CONDITIONAL PROBABILITY, INDEPENDENCE, TOTAL PROBABILITY, BAYES’ RULE •

ML PARAMETER ESTIMATION •

BINARY HYPOTHESIS TESTING •

MARKOV AND CHEBYSHEV INEQUALITIES •

FUNCTIONS OF RANDOM VARIABLES •