STATS 425 Lecture Notes - Lecture 5: Probability Mass Function, Random Variable, Bernoulli Distribution
Document Summary
Many random processes produce numbers called random variables. Examples of random variables: sum of two dice, the length of time you wait for a bus, the number of heads in 20 coin flips. A random variable, x, is a function from the sample space s to the real numbers, x is a rule which assigns a number x for each outcome s in s. A realization is a particular value taken by a random variable. 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) = p(x=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. A discrete distribution is a probability mass function with 0<=p(xi)<=1.
