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##### Learning Outcome Statements
 1. Introductiona. define a random variable, an outcome, and an event; b. identify the two defining properties of probability, including mutually exclusive and exhaustive events, and compare and contrast empirical, subjective, and priori probabilities; c. state the probability of an event in terms of odds for and against the event; 2. Unconditional, Conditional, and Joint Probabilitiesd. calculate and interpret conditional probabilities; 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occure. demonstrate the application of the multiplication and addition rules for probability; 4. Multiplication Rule for Independent Eventsf. compare and contrast dependent and independent events; 5. The Total Probability Ruleg. calculate and interpret an unconditional probability using the total probability rule; 6. Expected Value (Mean), Variance, and Conditional Measures of Expected Value and Varianceh. calculate and interpret the expected value, variance, and standard deviation of random variables; i. explain the use of conditional expectation in investment applications; j. interpret a probability tree and demonstrate its application to investment problems; 7. Expected Value, Variance, Standard Deviation, Covariances, and Correlations of Portfolio Returnsk. calculate and interpret the expected value, variance, standard deviation, covariances, and correlations of portfolio returns; 8. Covariance Given a Joint Probability Functionl. calculate and interpret covariance given a joint probability function; 9. Bayes' Formulam. calculate and interpret an updated probability using Bayes' formula; 10. Principles of Countingn. identify the most appropriate method to solve a particular counting problem and analyze counting problems using factorial, combination, and permutation concepts.
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