What is a probability mass function

Answer

A Probability Mass Function (PMF) is a function that gives the probability that a discrete random variable takes on a specific value.

1. Definition

For a discrete random variable X, the probability mass function assigns probabilities to each possible value of X. 

2.Properties of a PMF

I). Non-Negativity: This ensures we do not have a negative probability

$p(x)\ge 0\text{for all }x$

II). The total probability is equal to 1

$\sum _{x}p(x)=1$

$\mathrm{e}$

3.Example of a PMF

Assume the event of tossing a two sided fair coin. The probability of Head is equal to probability of a Tail.

The PMF is given by,

Let X= 1 for Heads and X=0 for Tails

$p(x)=\{\begin{array}{ll}\frac{1}{2},& x=0\\ \frac{1}{2},& x=1\\ 0,& \text{otherwise}\end{array}$

$p(x)=P(X=x)$

$p(x)=P(X=x)$

$p$

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