# Index of /faculty/kerns/video/STAT3743/100610

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.

2010-10-06 Wed

Quantile functions

Definition of quantile function:

Q(p) = min{x : F(x) >= p}, 0 < p < 1

Properties:

1. defined, finite for 0 < p < 1
2. left continuous
3. reflect F about line y=x (continuous case)
4. boundary limits exist but may be infinite

Special case: normal distribution

Define z_{α}

Examples

z0.025, z0.01, z0.005

### Functions of random variables

The idea

#### Discrete case

Make a table, accumulate probabilities

Example: X ~ `binom`, Y = something

#### PDF method

Introduce the formula and conditions

Intuitive formula

Example: X ~ `norm`, Y = linear transformation

Fact: if X is any norm then lin. trans. is also normal

Example: X ~ `norm`, Y = exp(X) (lognormal)

#### CDF method

Introduce the method

Example: X ~ `unif(0,1)`, Y = -ln(X) (exponential)

Probability Integral Transform

Why the PIT is important

Date: 2010-10-08 15:21:17 EDT

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