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Hypergeometric distribution

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Calculates the probability density, lower cumulative probability, and upper cumulative probability of the hypergeometric distribution.
Number of specific elements in a sample x 
x = 0, 1, 2, ..., x ≤ n
Sample size n 
n = 0, 1, 2, ..., n ≤ N
Number of target elements in the population M
M = 0, 1, 2, ...; x ≤ M
Population size N
N = 0, 1, 2, ...; M ≤ N
\(\normalsize Hypergeometric\ distribution\\ (1)\ probability\ mass\\ \hspace{30px}f(x,n,M,N)={\large\frac{{}_MC_x\ {}_{N-M}C_{n-x}}{{}_NC_n}}\\ (2)\ lower\ cumulative\ distribution\\ \hspace{30px}P(x,n,M,N)={\large\displaystyle \sum_{t=0}^{x}}f(t,n,M,N)\\ (3)\ upper\ cumulative\ distribution\\ \hspace{30px}Q(x,n,M,N)={\large\displaystyle \sum_{t=x}^{M}}f(t,n,M,N)\\ (4)\ expectation(mean):\hspace{10px}{\large\frac{nM}{N}}\\\)

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