# Types of RV’s and Properties

Tags | Properties |
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# Bernoulli

Heads or tails, with success rate $p$. (this is a piecewise function)

We can express the likelihood as a function (which allows for certain numerical analysis)

# Binomial

This is the number of success in $n$ trials given success probability $p$.

Here are some facts

- binomial RV is the sum of bernoulli RV's ($Ber(p) = Bin(1, p)$)

It follows that

Binomial distributions need not be symmetrical.

# Poisson

This is the distribution of $x$ events happening given that $\lambda$ events usually happen. It is the limit of $Bin(n, p)$ such that $np = \lambda$ and $n→ \infty$.

The stats are

# Geometric

This is the number of trials until the first success

As such:

# Negative Binomial

This is the number of trials until $r$ successes.

It is also the sum of $r$ geometric distributions, which means that

# Uniform

This is just a distribution with uniform probability between $\alpha, \beta$. The following are true:

# Exponential

This is the time until first success

The following are true:

Poisson and Exponentials are deeply connected. The poisson is events in a time, and exponential is time until an event.