- CFA Exams
- 2022 Level I
- Topic 1. Quantitative Methods
- Learning Module 4. Common Probability Distributions

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##### Learning Outcome Statements PDF Download

1. Introduction and Discrete Random Variablesa. define a probability distribution and compare and contrast discrete and continuous random variables and their probability functions;
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2. Probability Functiona. define a probability distribution and compare and contrast discrete and continuous random variables and their probability functions;
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3. Cumulative Distribution Functiona. define a probability distribution and compare and contrast discrete and continuous random variables and their probability functions;
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4. Discrete and Continuous Uniform Distributionc. describe the properties of a discrete uniform random variable, and calculate and interpret probabilities given the discrete uniform distribution function;
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5. Binomial Distributione. define the properties of a Bernoulli random variable and a binomial random variable, and calculate and interpret probabilities given the binomial distribution function; | |

6. Normal Distributionf. explain the key properties of the normal distribution;g. contrast a multivariate distribution and a univariate distribution, and explain the role of correlation in the multivariate normal distribution;
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7. The Standard Normal Distributioni. explain how to standardize a random variable;
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8. Shortfall Risk and Roy's Safety-First Criterionk. define shortfall risk, calculate the safety-first ratio, and identify an optimal portfolio using Roy's safety-first criterion; | |

9. The Lognormal Distributionl. explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices; | |

10. Continuously Compounded Rates of Returnm. calculate and interpret a continuously compounded rate of return, given a specific holding period return; | |

11. Student's t-, Chi-Square, and F-Distributionsn. describe the properties of the Student's t-distribution, and calculate and interpret its degrees of freedom;
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12. Monte Carlo Simulationp. describe Monte Carlo simulation. |

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