Computing...

Input:

binomial distribution | number of trials | n = 100000\nprobability of success | p = 0.0001


Statistical properties:

mean | 10.\nstandard deviation | 3.16212\nvariance | 9.999\nskewness | 0.31618\nkurtosis | 3.09995


Probability density function (PDF):

P (X = x) = piecewise | 0.0001^x 0.9999^(100000 - x) binomial(100000, x) | 0<=x<=100000\n0 | (otherwise)


Cumulative distribution function (CDF):

P (X<=x) = piecewise | betaregularized(0.0001, 1, floor(x) + 1, 100000 - floor(x)) | 0<=x<100000\n1 | x>=100000


Random sample from the distribution:

9  |  16  |  14  |  7  |  11

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