Probability mass function

Definition:

• PMF of a Discrete random variable X assigns probabilities to the possible values of the random variable:
  • $p_X:{\Omega }_X\to [0,1]$
  • $p_X(k)\to P(X=k)$
• $\{X=a\},a\in {\Omega }_X$ form a partition of $\Omega ⟹{\sum }_{k\in {\Omega }_X}{p}_X(k)=1$
• $p(a)=P(X=a)$
  • Every distribution has a PMF