Cheat Sheet Probability Distributions

F x x p x x 0 1 2 3 4 0 0 0 2 0 4 0 6 0 8 1 0 x cdf.

Cheat sheet probability distributions. When you work with continuous probability distributions the functions can take many forms. Gamma distribution notation gamma k. Pdf kx 1e x k i x 0 k. More generally p is said to be a probability distribution or measure if the following three axioms hold 1.

These include continuous uniform exponential normal standard normal z binomial approximation poisson approximation and distributions for the sample mean and sample proportion. A continuous distribution s probability function takes the form of a continuous curve and its random variable takes on an uncountably infinite number of possible values. Cumulative distribution function cdf gives the probability that a random variable is less than or equal to x. This means the set of possible values is written as an interval such as negative infinity to positive infinity zero to infinity or an interval like 0 10 which represents all real numbers from 0 to 10 including 0 and 10.

Probability cheat sheet distributions unifrom distribution notation u a b cdf x a b a for x2 a b pdf 1 b a for x2 a b expectation 1 2 a b variance 1 12 b a 2 mgf etb eta t b a story. Probability density function pdf mean standard deviation student s t distribution this distribution was first studied by william gosset who published under the pseudonym student. There will be a problem sheet partnered with this sheet. Cheat sheet for probability theory ingmar land 1 scalar valued random variables consider two real valued random variables rv x and y with the individual probabil ity distributions px x and py y and the joint distribution px y x y.

This is an 10 page probability cheatsheet compiled from harvard s introduction to probability course taught by joe blitzstein. The probability formula sheet summarizes important probability probability concepts formulas and distributions with figures examples and stories. Axiom 2 the probability that at least one of the elementary events in the entire sample space will occur is 1 i e. All intervals of the same length on the distribution s support are equally probable.

0 probability cheat sheet here i will summarise the results from probability required for this course. The probability distributions are probability mass functions pmf if the random variables take discrete.