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Unformatted text preview: ECE 5510: Random Processes Lecture Notes Fall 2008 Lecture 2 Today: (1) Events as Sets (2) Axioms and Properties of Prob ability (3) Experimental RSS Measurement Announcements: HW 1 assigned today, due a week from today. Please sign up for a date for your discussion item. The application assignment 1 is posted on the wiki / WebCT. For quicker browsing for nonWebCT items, my wiki is span. ece.utah.edu and then go to Teaching: ECE 5510. You can also get there from WebCT. 1 Events as Sets All probability is defined on sets. In probability, we call these sets events . A set is a collection of elements. In probability, we call these outcomes . Defn: Event A collection of outcomes. Order doesnt matter, and there are no duplicates. 1.0.1 Set Terminology vs. Probability Terminology Set Theory Probability Theory Probability Symbol universe sample space (certain event) S element outcome (sample point) s set event E disjoint sets disjoint events E 1 E 2 = null set null event 1.1 Introduction There are different ways to define an event (set): List them: A = { , 5 , 10 , 15 ,... } ; B = { Tails,Heads } As an interval: [0 , 1], [0 , 1), (0 , 1), ( a,b ]. Note overlap with coordinates! ECE 5510 Fall 2008 2 An existing event set name: N , R 2 , R n By rule: C = { x R : x } , D = { ( x,y ) R 2 : x 2 + y 2 < R 2 } . Note Y&G uses  instead of the colon :, which I find confusing. 1.1.1 Important Events Heres an important event: = {} , the null event or the empty set . Heres the opposite: S is used to represent the set of everything possible in a given context, the sample space . S = B above for the flip of a coin. S = { 1 , 2 , 3 , 4 , 5 , 6 } for the roll of a (6sided) die. S = { Adenine,Cytosine,Guanine,Thymine } for the nucleotide found at a particular place in a strand of DNA. S = C , i.e. nonnegative real numbers, for your driving speed (maybe when the cop pulls you over)....
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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 University of Utah.
 Fall '08
 Chen,R

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