# Index of /faculty/kerns/video/STAT3743/092210

STAT 3743 Daily Outline

# STAT 3743 Daily Outline

Up there should be four (4) files:

• `STAT3743_xxxxxx.3gp` (video for mobile phones)
• `STAT3743_xxxxxx.ogv` (video in Ogg format)
• `STAT3743_xxxxxx.pdf` (scanned lecture transcript)
• `STAT3743_xxxxxx.webm` (video in WebM format)

The `WebM` video is definitely the highest quality, but you need a compatible browser/player to watch it. See How to watch the video for instructions to get one.

2010-09-22 Wed

What does [Bayes' Rule] mean?

Example: misfiling assistants

### Random variables

Definition

Support set

Examples

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

## Discrete random variables

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

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

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