**External Resources** 1. [ProbStats](https://probstats.org/) for visual plots. 2. ProbOnto (Probability Distribution Ontology) for data about distributions and their relationships. 3. [[SIPMath 3.0]] for data structures for probability distributions. --- ## Probability Distributions - **Uniform** (a Die Roll) - **Binomial** (a Coin Flip) - **Poisson** (N Coins Flips) - **Normal** (Many Coin Flips) - **t-Distribution** - **Exponential** () - **Gamma** () Relationships - **Binomial → Poisson**: As n→∞,p→0,np=λn \to \infty, p \to 0, np = \lambdan→∞,p→0,np=λ. - **Binomial → Normal**: As n→∞,np and $n(1−p)n \to \infty$, np \text{ and } n(1-p)n→∞,np and n(1−p) are large. - **Poisson → Normal**: As λ\lambdaλ becomes large. **Exponential Family** $f(x∣θ)=h(x)exp(η(θ)T(x)−A(θ))$ ### Binomial Tossing a coin n times, how likely to get k heads? ### Poisson ### Normal ### Exponential --- ## Central Concepts - **Central Limit Theorem**