# Index of /faculty/kerns/video/STAT3743/100410

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.

2010-10-04 Mon

#### Continuous CDFs

• nondecreasing
• continuous function
• limits at infinity
• derivative of CDF is PDF

#### Expectation

• mean, variance, MGF

Examples

• finite support: `beta(4,1)`
• integral 1, probability, μ, σ
• infinite support: `exp(rate = 5)`
• integral 1, prob, μ, σ

### Continuous uniform distribution

PDF, CDF, notation, R code, MGF

Find the mean, variance

Special case: `unif(min = 0, max = 1)`

### Normal distribution

PDF, notation, R code

Standard normal: Z

φ, Φ

If X ~ `norm(m,s)` then Z = (X-m)/s ~ `norm(0,1)`

MGF of Z

MGF of X

MGF of Y = a + bX

68-95-99.7 (Empirical) Rule

Example: find P(a < X < b) for something, say, IQ

### Quantiles and the quantile function

Want to go in reverse: given area, find the IQ

Date: 2010-10-08 15:20:41 EDT

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