Hypergeometric distribution describes the frequency of experiments, which has three parameters: the number of repetitions n, the number of successful results nsuc and the total number of results ntot. For example, there are 10 red balls and 20 black balls in a bag, and 15 balls are taken out from it, where the number of red balls obeys the hypergeometric distribution of n=20, nsuc= 10 and ntot=30.
The binomial distribution describes the frequency of the experiment by playback, with only two parameters: the number of repetitions n and the probability of success p, for example, there are 10 red balls and 20 black balls in a bag. Take a ball out of it, record the color and put it back in the bag. Repeat 15 times, and the number of red balls drawn will obey N = 20, P = 10/( 10+20).
The probability distribution of the above two experiments is shown in the following figure. It should be noted that for K >；; In the case of 10, the probability of hypergeometric distribution P(X=k) is 0, because there are only 10 red balls in the bag, and the number of red balls taken out cannot exceed10; In binomial distribution, the ball is put back into the bag every time, so more than 10 red balls may be taken out.