STATS 425 Lecture Notes - Lecture 1: Probability Mass Function, Random Variable, Probability Distribution
Document Summary
Discrete random variables: x is discrete if its possible values form a finite or countable infinite set. If x is a discrete random variable then the probability mass function (pmf) of x is p(x) = Then p(xi)>0 and p(x) = 0 for all other values of x: the events x = xi for i = 1, 2, are disjoint with union s so the sum of all p(xi) = 1. Discrete distributions: a discrete distribution is a probability mass function with 0<=p(xi)<=1, we say that two random variables, x and y have the same distribution if they have the same pmf. If for all s in s, x(s) = y(s), then x=y. The cumulative distribution function: f(x) = p(x<=x) for negative infinity < x < infinity, fx(x) is the cdf of x and fy(y) is the cdf of y. 0<=f(x)<=1: f(x) is non decreasing, if x <=y then f(x) <= f(y)
