Common Probability Distributions (2025 Level I CFA Exam – Quantitative Methods – Module 4)

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Topic 1 – Quantitative Methods
Reading 4 – Common Probability Distributions
0:00 Introduction and Learning Outcome Statements
3:20 LOS: define a probability distribution and compare and contrast discrete and continuous random variables and their probability functions
10:06 LOS: calculate and interpret probabilities for a random variable given its cumulative distribution function
14:53 LOS: describe the properties of a discrete uniform random variable, and calculate and interpret probabilities given the discrete uniform distribution function
16:18 LOS: describe the properties of the continuous uniform distribution, and calculate and interpret probabilities given a continuous uniform distribution
19:18 LOS: describe the properties of a Bernoulli random variable and a binomial random variable, and calculate and interpret probabilities given the binomial distribution function
26:22 LOS: explain the key properties of the normal distribution
32:09 LOS: contrast a multivariate distribution and a univariate distribution, and explain the role of correlation in the multivariate normal distribution
33:06 LOS: calculate the probability that a normally distributed random variable lies inside a given interval
34:58 LOS: explain how to standardize a random variable
38:54 LOS: calculate and interpret probabilities using the standard normal distribution
42:39 LOS: define shortfall risk, calculate the safety-first ratio, and identify an optimal portfolio using Roy’s safety-first criterion
46:38 LOS: explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices
48:20 LOS: calculate and interpret a continuously compounded rate of return, given a specific holding period return
51:21 LOS: describe the properties of the Student’s t-distribution, and calculate and interpret its degrees of freedom
53:27 LOS: describe the properties of the chi-square distribution and the F-distribution, and calculate and interpret their degrees of freedom
56:02 LOS: describe Monte Carlo simulation