05pmf - EECS 501 PDFs AND PMFs AND MIXTURES Fall 2001 DEF:...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EECS 501 PDFs AND PMFs AND MIXTURES Fall 2001 DEF: A discrete random variable (rv) is a mapping x : countable set. DEF: A continuous random variable is a mapping x : uncountable set. WLOG: Countable range of discrete rv is 1-1 with Z =integers. DEF: The pmf (probability mass function) for a discrete rv x is Props: p x ( X ) = Pr [ x = X ]. We have: 0 p x ( X ) 1; X =- p x ( X ) = 1. For continuous rvs, use pdf (probability density function) f x ( X ). EX1: Discrete rv x=#heads in 3 independent flips of a fair coin. p x (0) = p x (3) = 1 8 ; p x (1) = p x (2) = 3 8 ; p x ( X ) = 0 otherwise. EX2: Geometric pmf: p x ( X ) = (1- a ) X- 1 a, X 1 , < a < 1. Note: X =1 (1- a ) X- 1 a = a/ (1- (1- a )) = 1 and 0 < (1- a ) X- 1 a < 1. Note: PDF (distribution) F x ( X ) for discrete rv x is piecewise constant (staircase) function with a countable number of discontinuities. But: Flip a fair coin. If heads, flip a 2 nd coin with Pr[heads]=2/3. If 2 nd coin heads, set rv x=3; if 2 nd coin tails, set rv x=1....
View Full Document

This note was uploaded on 07/22/2011 for the course EECS 370 taught by Professor Lehman during the Spring '10 term at University of Florida.

Page1 / 3

05pmf - EECS 501 PDFs AND PMFs AND MIXTURES Fall 2001 DEF:...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online