# Probability-Mass-Function

07-14-2022 || 23:49
Tags: #probability

# probability-mass-function

To define the probability distribution function for a discrete random variable we use the probability mass function.

Most of the time it is expressed as $P(x)$ for expressing the probability of x
In case of multiple variables, another way is to use, $P(x=1)$
Also another rare bur used notation is $x \sim P(x)$

To be a probability mass function, the function needs to satisfy the following conditions,

1. $P$ must be defined for all of the states possible of the discrete random variable
2. $\forall x 0 \leqslant P(x) \leqslant 0$
3. $\sum_{x} P(x) = 1$