binomialvariate
- binomialvariate(n=1, p=0.5)
Binomial random variable.
Gives the number of successes for *n* independent trials
with the probability of success in each trial being *p*:
sum(random() < p for i in range(n))
Returns an integer in the range:
0 <= X <= n
The integer is chosen with the probability:
P(X == k) = math.comb(n, k) * p ** k * (1 - p) ** (n - k)
The mean (expected value) and variance of the random variable are:
E[X] = n * p
Var[X] = n * p * (1 - p)© Python Software Foundation. PSF License Version 2 · Official docs ↗
1 Example
>>> # Six roulette wheel spins (weighted sampling with replacement) >>> choices(['red', 'black', 'green'], [18, 18, 2], k=6) ['red', 'green', 'black', 'black', 'red', 'black'] >>> # Deal 20 cards without replacement from a deck >>> # of 52 playing cards, and determine the proportion of cards >>> # with a ten-value: ten, jack, queen, or king. >>> deal = sample(['tens', 'low cards'], counts=[16, 36], k=20) >>> deal.count('tens') / 20 0.15 >>> # Estimate the probability of getting 5 or more heads from 7 spins >>> # of a biased coin that settles on heads 60% of the time. >>> sum(binomialvariate(n=7, p=0.6) >= 5 for i in range(10_000)) / 10_000 0.4169 >>> # Probability of the median of 5 samples being in middle two quartiles >>> def trial(): ... return 2_500 <= sorted(choices(range(10_000), k=5))[2] < 7_500 ... >>> sum(trial() for i in range(10_000)) / 10_000 0.7958
from the Python docs