Gaussian+pdf+and+special+properties

# Gaussian+pdf+and+special+properties - Gaussian...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Gaussian distribution: The analytical expression for a simple Gaussian pdf (commonly termed as the standard normal with zero mean and unit variance, i.e. (0,1) X N ∼ ): 2 2 2 2 1 pdf: ( ) , 2 1 cdf: ( ) ( ) ( ) 2 x X x x u X X f x e x F x f u du e du x π π − − −∞ −∞ = − ∞ < < + ∞ = = = Φ ∫ ∫ Note: • the special function ( ) x Φ table (only for the positive portion) can be found in many text books on Probability. The relation, ( ) 1 ( ) x x Φ − = − Φ , will help you to get ( ) x Φ for negative values of its variable. • Another special function defined as, 2 2 1 ( ) 2 u x Q x e du π +∞ − ∫ ¡ , measuring the areas in the tail portion of the Gaussian pdf, is commonly used in communication systems. • Relation between the two special functions: ( ) 1 ( ) x Q x Φ = − . Important Properties of a Gaussian r.v., (0,1) X N ∼ : { } { } { } ( ) { } ( ) { } { } { } { } { } { } 2 2 2 2 2 2 1 ( ) 0,--- zero-mean 2 1 1,--- unit-variance 2 1 1 1 68.3%68....
View Full Document

## This note was uploaded on 09/14/2011 for the course ECE 321 taught by Professor Hongyage during the Spring '11 term at NJIT.

### Page1 / 2

Gaussian+pdf+and+special+properties - Gaussian...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online