MAT 2377 Lecture Notes - Lecture 4: Random Variable, Probability Mass Function, Sample Space
9 May 2014
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Denition : let s be a sample space. A function x : s r, that associates a real number x(s) to each outcome s is called a random variable. Notation : the range of the random variable is denoted rx. Note : we use upper-case letter (often at the end of the alphabet) to denote random variables, e. g. x, y, z, w, . Note : as an outcome is observed and we evaluate the random variables, we obtain an observed value. The observed values are denoted with lower-case letters, e. g. x, y, z, w, . Example 1 : consider calls to a communication system. Let x be the number of calls between 8 am and 9 am. Events with random variables : we can construct events with random variables. Here are a few examples : let a r, we interpret {x a} as the following event :
