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