Lecture Notes 1 Basic Probability - Stanford University

Lecture Notes 1 Basic Probability Set Theory Elements of Probability Conditional Probability Sequential Calculation of Probability Total Probability and Bayes Rule Independence CountingEE 178/278A: Basic ProbabilityPage 1 1 Set Theory Basics A set is a collection of objects, which are itselements Ameans that is an element of the setA A set with no elements is called theempty set, denoted by Types of sets: Finite:A={ 1, 2, .. , n} Countably infinite:A={ 1, 2, ..}, , the set of integers uncountable : A set that takes a continuous set of values, , the[0,1]interval, the real line, etc. A set can be described by all having a certain property, ,A= [0,1]can bewritten asA={ : 0 1} A setB Ameans that every element ofBis an element ofA Auniversal set containsallobjects of particular interest in a particularcontext, , sample space for random experimentEE 178/278A: Basic ProbabilityPage 1 2 Set Operations Assume a universal set Three Basic operations: Complementation: A complement of a setAwith respect to isAc={ : / A}, so c= Intersection:A B={ : Aand B} Union:A B={ : Aor B} Notat

an uncountable number of points • Examples: Random number between 0 and 1: Ω = [0,1] Suppose we pick two numbers at random between 0 and 1, then the sample space consists of all points in the unit square, i.e., Ω = [0,1]2 1.0 1.0 x y EE 178/278A: Basic Probability Page 1–10

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