1. Basic Definitions *a. define a probability distribution and distinguish between discrete and continuous random variables and their probability functions;*
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b. describe the set of possible outcomes of a specified discrete random variable;*
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2. Probability Function *c. interpret a cumulative distribution function;*
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d. calculate and interpret probabilities for a random variable, given its cumulative distribution function;*
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3. Cumulative Distribution Function *c. interpret a cumulative distribution function;*
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d. calculate and interpret probabilities for a random variable, given its cumulative distribution function;*
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4. The Discrete Uniform Distribution *e. define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable;*
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f. calculate and interpret probabilities given the discrete uniform and the binomial distribution functions;*
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g. construct a binomial tree to describe stock price movement;*
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h. calculate and interpret tracking error;*
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i. define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution;*
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5. The Binomial Distribution *e. define a discrete uniform random variable, a Bernoulli random variable, and a binomial random variable;*
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f. calculate and interpret probabilities given the discrete uniform and the binomial distribution functions;*
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g. construct a binomial tree to describe stock price movement;*
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h. calculate and interpret tracking error;*
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i. define the continuous uniform distribution and calculate and interpret probabilities, given a continuous uniform distribution;*
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6. The Normal Distribution *j. explain the key properties of the normal distribution;*
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7. The Univariate and Multivariate Distributions *k. distinguish between a univariate and a multivariate distribution and explain the role of correlation in the multivariate normal distribution;*
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8. The Standard Normal Distribution *l. determine the probability that a normally distributed random variable lies inside a given interval;*
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m. define the standard normal distribution, explain how to standardize a random variable, and calculate and interpret probabilities using the standard normal distribution;*
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9. Shortfall Risk and Roy's Safety-First Criterion *n. define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy's safety-first criterion;*
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10. The Lognormal Distribution *o. explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices;*
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11. Discretely and Continuously Compounded Rates of Return *p. 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;*
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12. Monte Carlo Simulation *q. explain Monte Carlo simulation and describe its applications and limitations;*
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r. compare Monte Carlo simulation and historical simulation.*
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