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Cumulative Probability Function

Cumulative Probability Function

The cumulative probability function of a random variable (discrete or continuous) is a function whose domain is similar to that of the probability mass or density function, but whose range is the set of probabilities associated with the possibility that the random variable will assume a value that is less than or equal to the values in the domain. The cumulative probability function of a random variable X is denoted by FX(x) and is defined as

FX(x) = P (X £ x)

For a discrete random variable X with a probability mass function of pX(x), its cumulative probability function FX(x) is given by

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NOTE: A continuous random variable Y with a probability density function of fy(y) has a cumulative distribution function Fy(y) given by

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EX. The discrete random variable X that assumes the value of the roll of two dice has the following cumulative probability distribution.

x pX(x) FX(x)
2 1 / 36 1/36
3 2 / 36 3/36
4 3 / 36 6/36
5 4 / 36 10/36
6 5 / 36 15/36
7 6 / 36 21/36
8 5 / 36 26/36
9 4 / 36 30/36
10 3 / 36 33/36
11 2 / 36 35/36
12 1 / 36 1

Note that for x = 2, 3, 4, ..... , 12

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Subject: 
Statistics
Subject X2: 
Statistics

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