# MATH 302 Lecture Notes - Lecture 4: Cumulative Distribution Function, Random Variable

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Cumulative distribution function

All the different variables have a cumulative distribution function, which simply

adds up the probabilities of all the values of the variable below the particular

value of X. So if X = 3, then the cdf will be the probability of 1 + probability of 2 +

probability of 3.

Just like in a cumulative graph, it just provides the values of the cumulative

probabilities so far.

So for example,

The pdf of a function is equal for all values in the range and 0 otherwise. There

are 5 values in the range from 1 to 5 What is the cdf?

The cdf would be

X = 0 0

X = 1 0.20

X = 2 0.40

X = 3 0.60

X = 4 0.80

X = 5 1

X = 6,7,8 1

The cdf is represented by F(x)

The shape of the graph for a cdf of a discrete random variable

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