📈 Poisson Distribution The Poisson distribution models the number of events occurring in a fixed interval of time or space, assuming the events occur independently and at a constant average rate. ...

🎯 Negative Binomial Distribution The Negative Binomial distribution models the number of trials needed to achieve a fixed number of successes in independent Bernoulli trials. 📌 Definition Let $X...

🧮 Multinomial Distribution The Multinomial distribution generalizes the Binomial: it models the counts of outcomes in multiple categories from a fixed number of independent trials. 📌 Definition ...

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🧪 Hypergeometric Distribution The Hypergeometric distribution models the number of successes in a sample drawn without replacement from a finite population. 📌 Definition Let $X \sim \text{Hyperg...

🎲 Geometric Distribution The Geometric distribution models the number of trials until the first success in a sequence of independent Bernoulli trials. 📌 Definition Let $X \sim \text{Geometric}(p...

🎨 Categorical Distribution The Categorical distribution models a single draw from $k$ categories, each with its own probability. 📌 Definition Let $X \sim \text{Categorical}(\mathbf{p})$, where $...

🎯 Binomial Distribution The Binomial distribution models the number of successes in a fixed number of independent Bernoulli trials. 📌 Definition Let $X \sim \text{Binomial}(n, p)$, where $n$ is ...