# STA 2023 Chapter Notes - Chapter 4: Continuous Or Discrete Variable, Random Variable, Standard Deviation

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## Document Summary

A random variable is a variable that assumes numerical values associated with the random outcomes of an experiment, where one (and only one) is assigned to each sample point. Random variables that can assume a countable number of values are called discrete. Random variables that can assume values corresponding to any of the points contained in an interval are called continuous. The probability distribution of a discrete random variable is a graph, table, or formula that specifies the probability associated with each possible value that the random variable can assume. Requirements for the probability distribution of a discrete random variable x: p(x) 0 for all values of x, p(x) = 1 where the summation of p(x) is over all possible values of x. The mean, or expected value, of a discrete random variable x is. The variance of a random variable x is. 2 = e[(x - )2] = ( x - )2p(x) = x2p(x) - 2.

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