This document summarizes the probabilities of different distributions for various values. It provides the probabilities, expectations, variances, and standard deviations for: 1) A hypergeometric distribution with parameters N=25, N1=8, n=21, x=4. 2) A binomial distribution with parameters n=25, p=0.25, x=13. 3) A Poisson distribution with parameters λ=8, x=6.

1. Roberth Tampoa
25.149.524
Num.
Hipergeométrica Binomial Poisson
4 N = 25 n = 21 λ = 8
N1 = 8 p = 0,25
n = 6
x = 4 x = 13 x = 6
P(X=x) P(X=x) P(X=x)
Hipergeometrica
P(X=x) = (N1Cx) (N-N1Cn-x) (NCn)-1 for x = max (0, n-N+N1), ... , min (n, N1)
P(X = 4) = 0,053754940711
Expectation = nN1/N = 1,92
Variance = nN1(N - N1)(N - n) / [N2(N - 1)] = 1,0336
Standard deviation = 1,016661202171
Binomial

2. P(X=x) = (nCx) px (1-p)n-x for x = 0,1, ..., n
P(X = 13) = 0,000303566114
Expectation = np = 5,25
Variance = np(1 - p) = 3,9375
Standard deviation = 1,984313483298
Moment gener ating function M(t) = (1 - p + pet)n
Poisson
P(X=x) = e-
x / x! for x = 0, 1, ....
P(X = 6) = 0,050409406725
Expectation =  = 3
Variance =  = 3
Standard deviation = 1,732050807569
Moment generating function M(t) = exp[(et - 1)]