The probability of success is p.

The failure probability is q =1-p.

After n tests,

Its success expects E(X) to be p.

The variance D(X) is p( 1-p).

Binomial distribution

If the probability of an event is p

Then the probability of not happening is q =1-p.

The probability of appearing k times in n independent repeated tests is p (ξ = k) = c (n, k) * p k * (1-p) (n-k), where c (n, k) = n! /(k！ * (n-k)！ ) attention! The second equal sign is followed by a superscript in brackets, which means the power of the square.

Then say that this belongs to binomial distribution.

Where p is called the probability of success.

Write ξ~B(n, p)

Expected value: Eξ=np

Variance: Dξ=npq

Hypergeometric distribution

Hypergeometric distribution is a discrete probability distribution in statistics.

Describes the number of times to extract n objects from a limited number of objects, and successfully extract the specified type of objects (no return). In the sampling inspection of product quality, if there are m defective products in n products, the number of defective products obtained when sampling n products is X=k, and then P (X = K) = C (M K) C (N-M N-K)/C (N N N n), C(a b) is the combination of classical probabilities, a is the lower limit and b is the upper limit. At this time, we call it a random variable X.

The hypergeometric distribution model of 1 is non-return sampling.

2) The parameters in hypergeometric distribution are m, n, n.. Hypergeometric distribution is denoted as X~H(n, m, n).

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