Concept: In the sampling inspection of product quality, if there are m defective products in N products and the number of defective products obtained by sampling inspection of N products is X=k, then P(X=k), at this time, the random variable X is said to obey the hypergeometric distribution.
The model of hypergeometric distribution does not return sampling.
The parameters in hypergeometric distribution are m, n, n.
The above hypergeometric distribution is expressed as X~H(n, m, n).
Mathematical expectation: E(x)=nM/N
Variance: σ 2 = nm (n-m) (n-n)/[(n 2) (n-1)]
Binomial distribution: If the probability of an event is p and the experiment is repeated n times, the probability of the event happening k times is: p = c (k, n) × p k× (1-p) (n-k). C (k, n) represents the number of combinations, that is, the number of k methods of n things.
Mathematical expectation: E(x)=np
Variance: σ 2 = NP (1-p)
Extended data;
For fixed n and p, when k increases, the probability P{X=k} first increases until it reaches the maximum value, and then monotonically decreases. It can be proved that the general binomial distribution also has this property, and:
When (n+ 1)p is not an integer, the binomial probability P{X=k} reaches the maximum when k=[(n+ 1)p];
When (n+ 1)p is an integer, the binomial probability P{X=k} reaches the maximum when k=(n+ 1)p and k=(n+ 1)p- 1. ?
Baidu Encyclopedia-Binomial Distribution