# Types of Probability Distribution

Bernoulli and Uniform A distribution of type $20$-$0$-$0$, or $17$-$1$-$2$, is much less likely than a distribution of type $7$-$7$-$6$. The argument that says the probability Jack gets all the brownies is $(1/3)^{20}$ is perfectly correct.

Binomial and Hypergeometric What is the probability that there were 2 days with crashes on that week? =days with crashes The total elements are N=30 days, and the days with crashes are the bad, K=12.

Exponential and Weibull The probability distribution function of a Weibull distribution is as follows: $$f(x) = a\cdot b^{-a}x^{a-1}\cdot e^{(-x/b)^a},\quad x>0$$ for parameters $a,b>0$. I have to show that $X\sim\mathrm{Weibull}(a,b)$ iff $X^a\sim\mathrm{expo}(b^a)$.

image: itl.nist.gov
Gamma and Beta According to Wikipedia, the Beta distribution is related to the gamma distribution by the following relation: $$\lim_{n\to\infty}n B(k, n) = \Gamma(k, 1)$$ Can you point me to a derivation of thi...

Geometric and Negative Binomial The geometric distribution is a special case of the negative binomial distribution. It deals with the number of trials required for a single success. Thus, the geometric distribution is negative binomial distribution where the number of successes (r) is equal to 1.

source: stattrek.com
Normal, Log-Normal, Student's t, and Chi-Squared Distributions related to the normal distribution Three important distributions: Chi-square (˜2) distribution. tdistribution. Fdistribution. Before we discuss the ˜2;t, and F distributions here are few important things about the gamma distribution. The gamma distribution is useful in modeling skewed distributions for variables that are not negative.

source: stat.ucla.edu
Poisson Poisson Distribution. A Poisson distribution is the probability distribution that results from a Poisson experiment. Attributes of a Poisson Experiment. A Poisson experiment is a statistical experiment that has the following properties: The experiment results in outcomes that can be classified as successes or failures.

source: stattrek.com