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Unformatted text preview: ECE 5510: Random Processes Lecture Notes Fall 2009 Lecture 5 Today: (1) Expectation, (2) Families of discrete r.v.s • HW 2 due on Thursday. Office hours today until 1:15 pm. • Today’s reading: 2.5, 2.7, 2.8. Thursday’s reading: 3.13.5, 2.6, 3.7 0.1 Recap of Critical Material • A random variable (r.v.) is a mapping, X : S → R , where the range is S X ⊂ R . • For a 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 ]. • CDF, F X ( x ) is defined as F X ( x ) = P [ { X : X ≤ x } ]. 0.2 Expectation Section 2.5 of Y&G. Def’n: Expected Value The expected value of discrete r.v. X is E X [ X ] = summationdisplay x ∈ S X xP X ( x ) E X [ X ] is also referred to as μ X . It is a parameter which describes the ‘center of mass’ of the probability mass function. Note: Y&G uses E [ X ] to denote expected value. This is somewhat ambiguous, as we will see later. The first (subscript) X refers to the pmf we’ll be using, the second X refers to what to put before the pmf in the summation. Example: Bernoulli r.v. Expectation What is the E X [ X ], a Bernoulli r.v.? E X [ X ] = summationdisplay x ∈ S X xP X ( x ) = summationdisplay x =0 , 1 xP X ( x ) = (0) · P X (0)+(1) · P X (1) = p ECE 5510 Fall 2009 2 Example: Geometric r.v. Expectation What is the E T [ T ], a Geometric r.v.?...
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This note was uploaded on 09/15/2011 for the course ECE 5510 taught by Professor Chen,r during the Fall '08 term at Utah.
 Fall '08
 Chen,R

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