# STAT 1430 Lecture 13: Random Variables February 19,2019

## Document Summary

Setting things up: tree: in the tree, we can multiply branches to get and probabilities (which show on the leaves, p(a)*p(b|a)=p(a&b, p(a)*p(notb|a)=p(a¬b, p(nota)*p(b|nota)=p(nota&b, p(nota)*p(notb|nota)=p(nota¬b) Setting things up: table: can draw table from tree or can draw tree from table. If marginal and conditional probabilities are given=>tree is better/ easier. If and probabilities are given=>table is better/easier: does not always work >need enough information. Agenda: what a random variable is, discrete random variables, probability distributions, the mean of a random variable, rules for means, the variance of a random variable, rules for variances, standard deviation of a random variable. Random variable: definition, characteristic you can measure/count/categorize, notation: X=number of customers in a queue at the bank. X=time it takes to serve a customer at a help desk. Types of random variables: discrete random variable: Finite {0,1, , n} or countably infinite {0,1, 2, } like the whole numbers. Examples: number of throws to get 6 in a dice: continuous random variable: