Probability Mass Function

[!def] What is 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 $x \sim P(x)$

[!question] Conditions of Probability Mass Function

  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. $\sum_{x} P(x) = 1$