Question

how do you find the Probability mass function given a Culmative distribution function?

Answer 1

We know that,

Finding the PMF using CDF:-
We can get the PMF (i.e. the probabilities for P(X = xi)) from the CDF by determining the height of the jumps.
Specifically, because a CDF for a discrete random variable is a step-function with left-closed and right-open intervals, we have
P(X = xi) = F(xi) − limx ↑ xi F(xi)
and this expression calculates the difference between F(xi) and the limit as x increases to xi.

In this way we can find value of probability mass function P(xi) from the given Cumulative distribution function F(xi).

Thank you.