cs109 common distributions

bernoulli distribution

one trial, boolean that returns 1 if true and 0 otherwise

bernoulli parameters

p, representing probabiliity of success

bernoulii output

boolean (1 if success, 0 if fail)

binomial distribution

bernoulli w n trials. returns probability of success for a given # of trials.

binomial parameters

n = number of trials, p = probability of success

binomial output

probability of success for given number of trials or cdf up to that number

poisson distribution

probability of specific # of events occuring within a given time, distance, or space

poisson parameters

lambda, the true avg of the event happening over that specified interval

poisson output

the probability of the # of events occuring, or cdf up the # of events

geometric distribution

returns probability of the number of experiments it will take until you reach a success

geometric parameters

p, the probability of success for a single experiment

geometric output

the probability that it will take a specified number of trials to reach first occurence.

difference between geometric and binomial?

geometric asks about trials until first success, binomial asks about number of successes over many trials

negbin distribution

returns probability of a specified number of experiments until r successes, geometric w/ many trials

negbin parameters

r = # of successes, p = probability of success for each individual trial

hypergeometric distribution

the probability of getting k successes in n draws without replacement, from a finite population of size N that contains a known number of K total successes

categorical distributions

works the same as other number distributions, just with categories. no expectation, variance, or PMF.

uniform distribution (continuous)

equally likely to take on any value in its range (a, b). returns probability of getting a value in that range

exponential distribution (continuous)

returns probability that it will take a certain amount of time before the event occurs

uniform parameters

a, b = min, max of range

exponential parameter

lambda, average NUMBER of events that occur within the specified time

normal/gaussian distribution

returns how likely a specific value is to occur, given mean and variance

normal distribution parameters

mean, variance (std²)