Normal and Lognormal Distributions for SOA Exam P

Learn essential concepts of normal and lognormal distributions in this 21-minute tutorial designed for SOA Exam P preparation. Master the fundamentals of normal distribution, including its bell-shaped curve characteristics and how to define a normal random variable X ~ N(𝜇,𝜎^2). Explore standardization using Z-scores, probability calculations with standard normal distribution tables, and applications of the central limit theorem. Delve into lognormal distributions, understanding their skewed-right shape and relationship to normal distributions through the equation X=e^Y where Y ~ N(𝜇,𝜎^2). Calculate expected values, variance, higher moments, mode, median, and percentiles for both distribution types. Gain practical knowledge of transforming lognormal variables to normal variables using natural logarithms, preparing thoroughly for probability and univariate random variables sections of the actuarial exam.