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Cumulative Distribution Functions

A probability distribution tells you the probability of something happening,the probability of the random variabletaking the valueA Cumulative distribution tells you the probability of the random variabletaking a value less than or equal to a valueoften written

Given a probability distributionwe can find the cumulative distribution:

Ifis presented in a table, add the entries as you go along.

1

2

3

4

5

0.1

0.3

0.15

0.05

0.4

0.1

0.1+0.3=0.4

0.1+0.3+0.15=0.55

0.1+0.3+0.15+0.05=0.6

0.1+0.3+0.15+0.05+0.4=1

Ifis presented as a function, integrate. Supposethen

Given a cumulative distributionwe can find the probability distribution:

Ifis presented in a table, subtract successive entries as you go along.

1

2

3

4

5

0.1

0.4

0.55

0.6

1

0.1

0.4-0.1=0.3

0.55-0.4=0.15

0.6-0.55=0.05

1-0.6=0.4

Ifis presented as a function, differentiate. Supposethen