Cumulative Distribution Function From a Probability Mass Function and Vice Versa
We can construct the cumulative distribution for arandom variable where a random variable may only take certain discrete values  from the probability dens function.
Suppose the probability mass function for a random variable is
0 
1 
2 
3 

0.3 
0.2 
0.1 
0.4 
For the cumulative distribution functionm we want the values ofWe can obtain these by adding up the individual probabilities for values of up to and including We obtain
0 
1 
2 
3 

0.3 
0.3+0.2=0.5 
0.3+0.2+0.1=0.6 
0.3+0.2+0.1+0.4=1 
Conversely, given a cumulative distribution function we can construct the probability mass function using the formula
From the cumulative distribution function above
0 
1 
2 
3 

0.3 
0.50.3=0.2 
0.60.5=0.1 
10.6=0.4 
This returns the original probability mass function.