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##### Learning Outcome Statements
 1. Basic Definitionsa. define a probability distribution and distinguish between discrete and continuous random variables and their probability functions; b. describe the set of possible outcomes of a specified discrete random variable; 2. Probability Functionc. interpret a cumulative distribution function; d. calculate and interpret probabilities for a random variable, given its cumulative distribution function; 3. Cumulative Distribution Functionc. interpret a cumulative distribution function; d. calculate and interpret probabilities for a random variable, given its cumulative distribution function; 4. The Discrete Uniform Distributione. define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable; f. calculate and interpret probabilities given the discrete uniform and the binomial distribution functions; g. construct a binomial tree to describe stock price movement; h. calculate and interpret tracking error; i. define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution; 5. The Binomial Distributione. define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable; f. calculate and interpret probabilities given the discrete uniform and the binomial distribution functions; g. construct a binomial tree to describe stock price movement; h. calculate and interpret tracking error; i. define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution; 6. The Normal Distributionj. explain the key properties of the normal distribution; 7. The Univariate and Multivariate Distributionsk. distinguish between a univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution; 8. The Standard Normal Distributionl. determine the probability that a normally distributed random variable lies inside a given interval; m. define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution; 9. Shortfall Risk and Roy's Safety-First Criterionn. define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy's safety-first criterion; 10. The Lognormal Distributiono. explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices; 11. Discretely and Continuously Compounded Rates of Returnp. distinguish between discretely and continuously compounded rates of return and calculate and interpret a continuously compounded rate of return, given a specific holding period return; 12. Monte Carlo Simulationq. explain Monte Carlo simulation and describe its applications and limitations; r. compare Monte Carlo simulation and historical simulation.
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