explain the differences between a probability mass function and a probability density function. describe the four common population moments. understand and apply the concept of a mathematical expectation of a random variable. describe and distinguish a probability mass function from a cumulative distribution function and explain the relationship between these two. After completing this reading, you should be able to: a. Random Variables Global Association of Risk Professionals. distinguish between conditional and unconditional probabilities. define and calculate a conditional probability. calculate the probability of an event for a discrete probability function. explain the difference between independent events and conditionally independent events. describe independent events and mutually exclusive events. Fundamentals of Probability Global Association of Risk Professionals. LEARNING OBJECTIVES AND READING ASSIGNMENTS 12. Module 24.2: Bootstrapping and Random Number Generation Module 24.1: Monte Carlo Simulation and Sampling Error Reduction Module 23.2: Normal and Non-Normal Distributions

Module 23.1: Defining Returns and Volatility Reading 23: Measuring Return, Volatility, and Correlation Module 21.3: Autoregressive Moving Average (ARMA) Models Module 21.2: Autoregressive and Moving Average Models Module 20.1: Heteroskedasticity and Multicollinearity Module 19.2: Measures of Fit in Linear Regression Reading 19: Regression with Multiple Explanatory Variables Module 18.2: Ordinary Least Squares Estimation Module 16.2: Estimating Moments of the Distribution Module 16.1: Estimating Mean, Variance, and Standard Deviation Module 15.4: Independent and Identically Distributed Random Variables Module 15.3: Behavior of Moments for Bivariate Random Variables Module 15.2: Moments of Bivariate Random Distributions Module 15.1: Marginal and Conditional Distributions for Bivariate Distributions Reading 15: Multivariate Random Variables Module 14.3: Student’s t, Chi-Squared, and F-Distributions Module 14.2: Normal and Lognormal Distributions Module 14.1: Uniform, Bernoulli, Binomial, and Poisson Distributions Reading 14: Common Univariate Random Variables Module 13.3: Probability Density Functions, Quantiles, and Linear Transformations Module 13.2: Mean, Variance, Skewness, and Kurtosis Module 13.1: Probability Mass Functions, Cumulative Distribution Functions, and Expected Values Module 12.2: Conditional, Unconditional, and Joint Probabilities Learning Objectives and Reading Assignments

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