ISA 562 Lecture 15: Class 13 - Random Variables
4 Mar 2020
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Document Summary
Random variables are used in continuous sample spaces as well as in situations where we need to know more metrics. A random variable r on a probability space is a total function whose domain is the sample space, i. e. r : s sr. Usually, the codomain is subset of real numbers, i. e. variable" is a misnomer as this is a function. An indicator random variable maps each outcome to 0 or 1: M = 1 when all three tosses are the same, and 0 otherwise: This indicator partitions the sample space into two subsets as follows. (hht ) E s partitions the sample space into two subsets: E is naturally associated with the random indicator variable. E is the event when all three tosses match. The random variable partitions the sample space based on its values. For example, the random variable c introduced earlier defines the following event:
