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STAT 3743 Daily Outline

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2010-09-22 Wed

What does [Bayes' Rule] mean?

Example: misfiling assistants

Random variables

Definition

Support set

Examples

toss coin n times
toss coin until heads
toss coin, wait until lands

Discrete random variables

Tools of the trade

Definition

Probability mass functions (PMFs)

Every PMF satisfies…

Example: toss coin four times, X = #Heads

set up function, find PMF, draw graph

Mean, variance, standard deviation

calculate mean for previous example

Remarks

μ can be any number
μ is measure of center
interpretation

Cumulative distribution functions (CDFs)

Definition

Properties

nondecreasing
right-continuous
limits at infinity

Example: toss coin 3 times

find CDF

Discrete uniform distribution

Definition, PMF, notation

Examples

Find mean and variance of =disunif=(m)

Example: find mean/variance for rolling die

Bernoulli/Binomial model

Bernoulli model

Mean and variance

Binomial model

n Bernoulli trials
trials independent
prob p doesn't change

Definition, PMF, notation

Check sum of f(x) is 1

Binomial series

Find mean, variance of =binom=(n,p)

Example: five child family

How to do it with R

Example: roll 15 dice

Find/plot binomial CDFs

Connection to distr*** family of packages

Author: G. Jay Kerns <gkerns@ysu.edu>

Date: 2010-10-08 15:19:16 EDT

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