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* What a shitty misnomer
write out functions=====Standard Normal=====* <math>Z \sim N(0, expectation 1)</math>* <math>f(z) = \frac{1}{ \sqrt{2 \pi} } \textrm{exp} \left( - \frac{z^2}{2} \right) </math>* <math>E[X] = 0</math>* <math>Var[X] = 1</math> =====Parameterized Normal with mu and variancesigma=====* <math>Z \sim N(\mu,\sigma^2)</math>* <math>f( x | \mu, \sigma^2 ) = \frac{1}{ \sqrt{2 \pi \sigma^2} } \textrm{exp} \left( - \frac{ (x - \mu)^2 }{2 \sigma^2} \right) </math> ==== t distribution ====* Use if you don't know the true value of sigma. Replacing with sample standard deviation causes* Uses gamma distribution
pass* Total waiting time for all events to occur, for more than in random variable with an exponential distribution.
pass* Used for random variables which take on values between 0 and 1. Commonly used to model probabilities.
→Probability Distributions
** PMF for discrete and probability density function (PDF) if continuous. Can view everything as a density, though.
===DiscreteDistributions===
====Bernoulli====
* Binomial approximation standard score - how many standard deviations an observation is above or below the mean.
====Geometric====* The number of trials to observe a success ====Multinomial====* Generalize bernoulli and binomial to more than one possible outcome ====Poisson====* Used for counts* parameter <math>\lambda \gt 0</math> is the rate at which we expect to observe the thing we are counting ===ContinuousDistributions===
* Integral from -inf to inf = 1: "The probability that something happens = 1"
* f(x) >= 0: Densities are non-negative for all possible values of x
====Exponential====
* E.g, a bus that comes every 10 minutes, the exponential is your waiting time
* Rate parameter <math>\lambda</math>
* <math>E[X] = \frac{1}{\lambda}</math>
* <math>Var[X] = \frac{1}{\lambda^2}</math>
====Normal====
====Gamma====
====Beta====
==Tests for Categorical Data==
