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

STAT 3743 Daily Outline

STAT 3743 Daily Outline

Up there should be four (4) files:

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


  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}


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

Author: G. Jay Kerns <>

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

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