Cumulative Distribution Functions
A probability distribution tells you the probability of something happening,
the probability of the random variable
taking the value
A Cumulative distribution tells you the probability of the random variabletaking a value less than or equal to a value
often written
Given a probability distribution
we 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. Suppose
then
Given a cumulative distribution
we 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
