lecture05 - ECE 5510: Random Processes Lecture Notes Fall...

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Unformatted text preview: ECE 5510: Random Processes Lecture Notes Fall 2008 Lecture 5 Today: (1) pmf / CDF, (2) Expectation, (3) Families of r.v.s Homework 1 is graded, and solutions are posted on WebCT. HW 2 due on Thursday. Office hours today until 1:15pm. Appl. Assignment 1 drop-box is on WebCT: Put all results / Matlab code in one file. Due Tue 16th. Todays reading: 2.1-2.7. Thursdays reading: 3.1-3.5, 3.7 1 Discrete Random Variables A random variable (r.v.) is a mapping, X : S R , where the range is S X R . Discrete r.v., the range S X is countable. pmf: P X ( x ) = P [ { s S : X ( s ) = x } ] = P [ X ( s ) = x ] = P [ X = x ]. 1.1 Cumulative Distribution Function (CDF) Defn: Cumulative Distribution Function (CDF) The CDF, F X ( x ) is defined as F X ( x ) = P [ { X : X x } ]. Properties of the CDF: 1. F X ( x ) = { u S X : u x } P X ( x ). 2. lim x + F X ( x ) = 1, and lim x F X ( x ) = 0. 3. For all b a , F X ( b ) F X ( a ) ( the CDF is non-increasing ) Specifically, F X ( b )- F X ( a ) = P [ { a < X b } ]....
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lecture05 - ECE 5510: Random Processes Lecture Notes Fall...

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