## 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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## Random Variables and Expectation

Often we are interested in the magnitude of an outcome as well as its probability. E.g. in a gambling game amount you win or loss is as important as the probability each outcome.

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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 ## Probability and Set Operations

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We want to calculate probabilities for different events. Events are sets of outcomes, and we recall that there are various ways of combining sets. The current section is a bit abstract but will become more useful for concrete calculations later.

## What is Probability?

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I throw a coin $100$ times. I got $52$ heads.

## Probability: a short introduction

Next semester, I will teach a short course on Probability for university students who have not taken probability before, who know some basic mathematics, but who are not necessarily going to be studying mathematic.

The notes for this are here: