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.

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