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Probability Mass Function

Definition (Probability mass function)

Let XX be a discrete random variable with range X={x1,...}\mathscr{X}=\{x_1,...\}. The pmf of XX is the function p:R→Rp:\mathbb{R}\to\mathbb{R} defined by: p(x):= P(X=x), x∈Xp(x)= 0, x∉X\begin{align*}p(x):=\ &P(X=x),\ &&x\in\mathscr{X}\\p(x)=\ &0, \ &&x\notin\mathscr{X}\end{align*}

Lemma

  1. p(x)≥0 ∀x∈Xp(x)\ge 0 \ \forall x\in\mathscr{X}
  2. ∑x∈Xp(x)=1\sum_{x\in\mathscr{X}}p(x)=1

Linked from

MCMC

Monte Carlo Method

Prior

Shannon Coding Theorem

Shannon-Fano-Elias Code

Divergence Bound on KT

Penalty Lemma

Type

Channel Coding Operation

Asymptotic Equipartition Property

Convexity or Concavity of Information Measure

Cross-Entropy

Discrete Memoryless Source

Divergence

Entropy

Jensen-Shannon Divergence

Renyi Divergence

Stationary & Ergodic Source

Stationary Distribution

Expectation of a Function of a Random Variable

Expectation

Variance

Conditional probability function

Joint probability function

Marginal probability function

Probability Mass Function

Binomial Random Variable

Geometric Random Variable

Negative Binomial RV

Poisson Random Variable

Detailed Balance

Markov chain

Dirac Distribution