2 - Statistical Concepts

Summary

The probability density function for discrete and continuous random variances is defined, and related to the probability concepts from Chapter 1. The cumulative distribution function is introduced and its properties are outlined. The inverse cumulative distribution function is explained, leading to the quantiles of a distribution. The characteristic function and conditional probability distribution are defined, and their applications are explained. The important concepts of independent and exchangeable random variables are specified; the latter underlies the nonparametric and resampling estimators described in later chapters. Transformation of a distribution between functions of a random variable is illustrated . Key population measures of location, dispersion, shape, direction and association are described. The conditional expected value and variance are defined, leading to the Laws of Total Expectation, Variance and Covariance. The Markov, Chebyhev and Hoeffding's probability inequalities used throughout statistics are derived, and the concept of convergence of random variables is elucidated.