STAT 3201 Lecture Notes - Lecture 22: Probability Mass Function, Random Variable, Mutual Exclusivity
10 Apr 2017
School
Department
Course
Professor
Document Summary
Marginal and conditional probability distributions, independent random variables. Marginal probability mass and density functions: definition 1: let y1 and y2 be jointly discrete random variables with probability mass function p(y1, y2). Then, the marginal probability mass functions of y1 and y2: definition 2: let y1 and y2 be jointly continuous random variables with joint density function f(y1, y2). Then, the marginal density functions of y1 and y2: the term marginal has intuitive sense in these distributions. We accumulate probabilities (or marginalize) over the y1 or y2 axis. Examples: example: from a group of three republicans, two democrats, and one independent, a committee of two people is to be randomly selected. Republicans and y2 denote the number of democrats on the committee. Find the joint probability mass function of y1 and y2 and then find marginal probability mass functions of y1 and y2: find the marginal density functions of y1 and y2. Conditional probability distributions: start with the discrete case.
