>>> random()                             # Random float:  0.0 <= x < 1.0

0.37444887175646646

>>> uniform(2.5, 10.0)                   # Random float:  2.5 <= x < 10.0

3.1800146073117523

>>> expovariate(1 / 5)                   # Interval between arrivals averaging 5 seconds

5.148957571865031

>>> randrange(10)                        # Integer from 0 to 9 inclusive

7

>>> randrange(0, 101, 2)                 # Even integer from 0 to 100 inclusive

26

>>> choice([‘win‘, ‘lose‘, ‘draw‘])      # Single random element from a sequence

‘draw‘

>>> deck = ‘ace two three four‘.split()

>>> shuffle(deck)                        # Shuffle a list

>>> deck

[‘four‘, ‘two‘, ‘ace‘, ‘three‘]

>>> sample([10, 20, 30, 40, 50], k=4)    # Four samples without replacement

[40, 10, 50, 30]

>>> # 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

>>> # (a ten, jack, queen, or king).

>>> deck = collections.Counter(tens=16, low_cards=36)

>>> seen = sample(list(deck.elements()), k=20)

>>> seen.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.

>>> trial = lambda: choices(‘HT‘, cum_weights=(0.60, 1.00), k=7).count(‘H‘) >= 5

>>> sum(trial() for i in range(10000)) / 10000

0.4169

>>> # Probability of the median of 5 samples being in middle two quartiles

>>> trial = lambda : 2500 <= sorted(choices(range(10000), k=5))[2]  < 7500

>>> sum(trial() for i in range(10000)) / 10000

0.7958

# http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm

from statistics import mean

from random import choices

data = 1, 2, 4, 4, 10

means = sorted(mean(choices(data, k=5)) for i in range(20))

print(f‘The sample mean of {mean(data):.1f} has a 90% confidence ‘

      f‘interval from {means[1]:.1f} to {means[-2]:.1f}‘)

# Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson

from statistics import mean

from random import shuffle

drug = [54, 73, 53, 70, 73, 68, 52, 65, 65]

placebo = [54, 51, 58, 44, 55, 52, 42, 47, 58, 46]

observed_diff = mean(drug) - mean(placebo)

n = 10000

count = 0

combined = drug + placebo

for i in range(n):

    shuffle(combined)

    new_diff = mean(combined[:len(drug)]) - mean(combined[len(drug):])

    count += (new_diff >= observed_diff)

print(f‘{n} label reshufflings produced only {count} instances with a difference‘)

print(f‘at least as extreme as the observed difference of {observed_diff:.1f}.‘)

print(f‘The one-sided p-value of {count / n:.4f} leads us to reject the null‘)

print(f‘hypothesis that there is no difference between the drug and the placebo.‘)

from random import expovariate, gauss

from statistics import mean, median, stdev

average_arrival_interval = 5.6

average_service_time = 5.0

stdev_service_time = 0.5

num_waiting = 0

arrivals = []

starts = []

arrival = service_end = 0.0

for i in range(20000):

    if arrival <= service_end:

        num_waiting += 1

        arrival += expovariate(1.0 / average_arrival_interval)

        arrivals.append(arrival)

    else:

        num_waiting -= 1

        service_start = service_end if num_waiting else arrival

        service_time = gauss(average_service_time, stdev_service_time)

        service_end = service_start + service_time

        starts.append(service_start)

waits = [start - arrival for arrival, start in zip(arrivals, starts)]

print(f‘Mean wait: {mean(waits):.1f}.  Stdev wait: {stdev(waits):.1f}.‘)

print(f‘Median wait: {median(waits):.1f}.  Max wait: {max(waits):.1f}.‘)