- CFA Exams
- 2023 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 Variablesdefine a probability distribution and compare and contrast discrete and continuous random variables and their probability functions;calculate and interpret probabilities for a random variable given its cumulative distribution function; | |

2. Probability Functiondefine a probability distribution and compare and contrast discrete and continuous random variables and their probability functions;calculate and interpret probabilities for a random variable given its cumulative distribution function; | |

3. Cumulative Distribution Functiondefine a probability distribution and compare and contrast discrete and continuous random variables and their probability functions;calculate and interpret probabilities for a random variable given its cumulative distribution function; | |

4. Discrete and Continuous Uniform Distributiondescribe the properties of a discrete uniform random variable, and calculate and interpret probabilities given the discrete uniform distribution function;describe the properties of the continuous uniform distribution, and calculate and interpret probabilities given a continuous uniform distribution; | |

5. Binomial Distributiondescribe the properties of a Bernoulli random variable and a binomial random variable, and calculate and interpret probabilities given the binomial distribution function; | |

6. Normal Distributionexplain the key properties of the normal distribution;contrast a multivariate distribution and a univariate distribution, and explain the role of correlation in the multivariate normal distribution; calculate the probability that a normally distributed random variable lies inside a given interval; | |

7. The Standard Normal Distributionexplain how to standardize a random variable;calculate and interpret probabilities using the standard normal distribution; | |

8. Shortfall Risk and Roy's Safety-First Criteriondefine shortfall risk, calculate the safety-first ratio, and identify an optimal portfolio using Roy's safety-first criterion; | |

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

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

11. Student's t-, Chi-Square, and F-Distributionsdescribe the properties of the Student's t-distribution, and calculate and interpret its degrees of freedom;describe the properties of the chi-square distribution and the F-distribution, and calculate and interpret their degrees of freedom; | |

12. Monte Carlo Simulationdescribe Monte Carlo simulation. |

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