Discrete Probability Distribution

Junlin Liu
Sep 23, 2021


Probability mass function -> Discrete (finite number of different values)

Probability density function -> Continuous (every value in an interval)

Both have cumulative distribution function, where f(x) = P(X<x)

The inverse of the CDF is called quantile function, and it is useful for indicating where the probability is located in a distribution.

Discrete Distributions

f(x) are all probability mass function(pmf)

Discrete Uniform Distribution

Bernoulli Distribution

A sequence of Bernoulli trials -> Binomial Distribution

Large enough n can use normal distribution to estimate

If N is large and P is small, we can expect B(n,p) = Poisson(λ) and λ = n * p

Poisson in this case can be an alternative

Geometric Distribution

Negative Binomial Distribution

Poisson Distribution

x = occurrence of event given a time period

Hypergeometric Distribution

Sampling without replacement, exact n number of successes.

With replacement is binomial distribution.

Multinomial Distribution



Junlin Liu

Data Scientist in Finance. Take care of the memories, polish knowledge.