How to calculate binomial distribution in Python

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Binomial distribution in statistics is a type of discrete probability distribution, modeling the probability of success times among a predetermined Bernoulli process. A Bernoulli process is a binary experiment with result success or fail, in which the probability of success or fail is constant for each independent trial. The most striking point for a binomial distribution is the probability associated with discrete success number, 1,2,3,,,, until N, which is the trial size. In Python, binomial distribution probability can be calculated using pmf() function from scipy.stats.binom module. Say, we are interested in N = 25 Bernoulli process with success rate 0.15 for each trial. The following code shows the calculation of probability for every possible success count from 0 to 25.

#total 15 Bernoulli trial, with success probability 0.15 for each trial
n= 15
p = 0.15
#a list for integer 0 to n
sn = list(range(n + 1))
#calculate probability for each count number, and store in a list
pn = [binom.pmf(s, n, p) for s in sn ]
#print out each possible count and their corresponding probability
for i in range(n + 1):
    print(str(sn[i]) + "\t" + str(pn[i]))
#output
r p(r)
0 0.08735421910125173
1 0.2312317564444899
2 0.28563922854907725
3 0.21842999830223525
4 0.11563941086588901
5 0.0448953006891098
6 0.01320450020267937
7 0.0029959790375827166
8 0.0005287021831028324
9 7.256696630823176e-05
10 7.68356113851866e-06
11 6.163284335710162e-07
12 3.625461373947157e-08
13 1.4764322337341365e-09
14 3.722098068237306e-11
15 4.378938903808602e-13
#sum the value for all probabilities
sum(pn)
#result is one, verified that it is correct
1.0000000000000033

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