3, multi-dimensional distributed random variables
(1) a number of distribution
See https://blog.csdn.net/jteng/article/details/54632311
A number of extensions to the binomial distribution, the binomial distribution is univariate, multivariate and distributed a number of distributions.
Only two binomial test results for each test, and each test will have distributed a number of many possibilities, so many times after the test, a number of distribution describes the number of occurrences of each possible is the joint probability distribution .
(2) Gamma function
First talk about the difference between the prior probability and posterior probability of , and then the following steps:
Pretest probability is the probability often said;
Posterior probability is a conditional probability, conditional probability but not necessarily posterior probability;
We used Bayesian formula is the formula for the probability of seeking to delay the pretest probability;
As a simple example: a red ball pocket has three, two white balls, touch taken without replacement, requirements:
probability ⑴ red ball first touch (referred to as A),;
⑵ second touch the probability red ball (referred to as B),;
⑶ known second red ball touched, the first touch is seeking probability red ball.
solution:
⑴ P (A) = 3/ 5, which is pretest probability;
⑵ P (B) = P (A) P (B | A) + P (Inverse A) P (B | A reverse) = (3/5 ) × (1/2) + (2/5) × (3/4) = of 3/5
⑶ P (A | B) = P (A) P (B | A) / P (B) = (. 3 / 5) × (1/2) / ( 3/5) = 1/2, which is the posterior probability.
Beta distribution to Dirichlet distribution of the domain [0,1] are, in real life, Beta distribution is described univariate distribution, Dirichlet distribution is described multivariate distributions.
Ever since, Beta distribution can be used as the prior probability of the binomial distribution , Dirichlet distribution as the prior probability distribution of the number .
Since the two distributions are used the Gamma function, you must first understand the Gamma function.
Gamma function is the expression 
where, x> 0
Gamma function has the following properties:
DETAILED derived as follows:
Gamma function has played a role in the normalization of the Beta distribution and Dirichlet distribution.
1) Beta distribution
With continuous random variable distribution different, Beta distribution describes a probability distribution is defined on the interval [0,1] is a random variable, by two parameters