## Continuous Probability Distributions

We consider distributions that have a continuous range of values. Discrete probability distributions where defined by a probability mass function. Analogously continuous probability distributions are defined by a probability density function.

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## Discrete Probability Distributions

There are some probability distributions that occur frequently. This is because they either have a particularly natural or simple construction. Or they arise as the limit of some simpler distribution. Here we cover

• Bernoulli random variables
• Binomial distribution
• Geometric distribution
• Poisson distribution.

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## Counting Principles

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Counting in Probability. If each outcome is equally likely, i.e. $\mathbb P( \omega ) = p$ for all $\omega \in \Omega$, then since

(where $|\Omega|$ is the number of outcomes in the set $\Omega$ ) it must be that