Doc/library/random.rst
!random --- Generate pseudo-random numbers.. module:: random :synopsis: Generate pseudo-random numbers with various common distributions.
Source code: :source:Lib/random.py
This module implements pseudo-random number generators for various distributions.
For integers, there is uniform selection from a range. For sequences, there is uniform selection of a random element, a function to generate a random permutation of a list in-place, and a function for random sampling without replacement.
On the real line, there are functions to compute uniform, normal (Gaussian), lognormal, negative exponential, gamma, and beta distributions. For generating distributions of angles, the von Mises distribution is available.
Almost all module functions depend on the basic function :func:.random, which
generates a random float uniformly in the half-open range 0.0 <= X < 1.0.
Python uses the Mersenne Twister as the core generator. It produces 53-bit precision
floats and has a period of 2**19937-1. The underlying implementation in C is
both fast and threadsafe. The Mersenne Twister is one of the most extensively
tested random number generators in existence. However, being completely
deterministic, it is not suitable for all purposes, and is completely unsuitable
for cryptographic purposes.
The functions supplied by this module are actually bound methods of a hidden
instance of the :class:random.Random class. You can instantiate your own
instances of :class:Random to get generators that don't share state.
Class :class:Random can also be subclassed if you want to use a different
basic generator of your own devising: see the documentation on that class for
more details.
The :mod:!random module also provides the :class:SystemRandom class which
uses the system function :func:os.urandom to generate random numbers
from sources provided by the operating system.
.. warning::
The pseudo-random generators of this module should not be used for
security purposes. For security or cryptographic uses, see the
:mod:secrets module.
.. seealso::
M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator", ACM Transactions on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3--30 1998.
Complementary-Multiply-with-Carry recipe <https://code.activestate.com/recipes/576707-long-period-random-number-generator/>_ for a compatible alternative
random number generator with a long period and comparatively simple update
operations.
.. note::
The global random number generator and instances of :class:Random are thread-safe.
However, in the free-threaded build, concurrent calls to the global generator or
to the same instance of :class:Random may encounter contention and poor performance.
Consider using separate instances of :class:Random per thread instead.
.. function:: seed(a=None, version=2)
Initialize the random number generator.
If a is omitted or None, the current system time is used. If
randomness sources are provided by the operating system, they are used
instead of the system time (see the :func:os.urandom function for details
on availability).
If a is an int, its absolute value is used directly.
With version 2 (the default), a :class:str, :class:bytes, or :class:bytearray
object gets converted to an :class:int and all of its bits are used.
With version 1 (provided for reproducing random sequences from older versions
of Python), the algorithm for :class:str and :class:bytes generates a
narrower range of seeds.
.. versionchanged:: 3.2 Moved to the version 2 scheme which uses all of the bits in a string seed.
.. versionchanged:: 3.11
The seed must be one of the following types:
None, :class:int, :class:float, :class:str,
:class:bytes, or :class:bytearray.
.. function:: getstate()
Return an object capturing the current internal state of the generator. This
object can be passed to :func:setstate to restore the state.
.. function:: setstate(state)
state should have been obtained from a previous call to :func:getstate, and
:func:setstate restores the internal state of the generator to what it was at
the time :func:getstate was called.
.. function:: randbytes(n)
Generate n random bytes.
This method should not be used for generating security tokens.
Use :func:secrets.token_bytes instead.
.. versionadded:: 3.9
.. function:: randrange(stop) randrange(start, stop[, step])
Return a randomly selected element from range(start, stop, step).
This is roughly equivalent to choice(range(start, stop, step)) but
supports arbitrarily large ranges and is optimized for common cases.
The positional argument pattern matches the :func:range function.
Keyword arguments should not be used because they can be interpreted
in unexpected ways. For example randrange(start=100) is interpreted
as randrange(0, 100, 1).
.. versionchanged:: 3.2
:meth:randrange is more sophisticated about producing equally distributed
values. Formerly it used a style like int(random()*n) which could produce
slightly uneven distributions.
.. versionchanged:: 3.12
Automatic conversion of non-integer types is no longer supported.
Calls such as randrange(10.0) and randrange(Fraction(10, 1))
now raise a :exc:TypeError.
.. function:: randint(a, b)
Return a random integer N such that a <= N <= b. Alias for
randrange(a, b+1).
.. function:: getrandbits(k)
Returns a non-negative Python integer with k random bits. This method
is supplied with the Mersenne Twister generator and some other generators
may also provide it as an optional part of the API. When available,
:meth:getrandbits enables :meth:randrange to handle arbitrarily large
ranges.
.. versionchanged:: 3.9 This method now accepts zero for k.
.. function:: choice(seq)
Return a random element from the non-empty sequence seq. If seq is empty,
raises :exc:IndexError.
.. function:: choices(population, weights=None, *, cum_weights=None, k=1)
Return a k sized list of elements chosen from the population with replacement.
If the population is empty, raises :exc:IndexError.
If a weights sequence is specified, selections are made according to the
relative weights. Alternatively, if a cum_weights sequence is given, the
selections are made according to the cumulative weights (perhaps computed
using :func:itertools.accumulate). For example, the relative weights
[10, 5, 30, 5] are equivalent to the cumulative weights
[10, 15, 45, 50]. Internally, the relative weights are converted to
cumulative weights before making selections, so supplying the cumulative
weights saves work.
If neither weights nor cum_weights are specified, selections are made
with equal probability. If a weights sequence is supplied, it must be
the same length as the population sequence. It is a :exc:TypeError
to specify both weights and cum_weights.
The weights or cum_weights can use any numeric type that interoperates
with the :class:float values returned by :func:random (that includes
integers, floats, and fractions but excludes decimals). Weights are assumed
to be non-negative and finite. A :exc:ValueError is raised if all
weights are zero.
For a given seed, the :func:choices function with equal weighting
typically produces a different sequence than repeated calls to
:func:choice. The algorithm used by :func:choices uses floating-point
arithmetic for internal consistency and speed. The algorithm used
by :func:choice defaults to integer arithmetic with repeated selections
to avoid small biases from round-off error.
.. versionadded:: 3.6
.. versionchanged:: 3.9
Raises a :exc:ValueError if all weights are zero.
.. function:: shuffle(x)
Shuffle the sequence x in place.
To shuffle an immutable sequence and return a new shuffled list, use
sample(x, k=len(x)) instead.
Note that even for small len(x), the total number of permutations of x
can quickly grow larger than the period of most random number generators.
This implies that most permutations of a long sequence can never be
generated. For example, a sequence of length 2080 is the largest that
can fit within the period of the Mersenne Twister random number generator.
.. versionchanged:: 3.11 Removed the optional parameter random.
.. function:: sample(population, k, *, counts=None)
Return a k length list of unique elements chosen from the population sequence. Used for random sampling without replacement.
Returns a new list containing elements from the population while leaving the original population unchanged. The resulting list is in selection order so that all sub-slices will also be valid random samples. This allows raffle winners (the sample) to be partitioned into grand prize and second place winners (the subslices).
Members of the population need not be :term:hashable or unique. If the population
contains repeats, then each occurrence is a possible selection in the sample.
Repeated elements can be specified one at a time or with the optional
keyword-only counts parameter. For example, sample(['red', 'blue'], counts=[4, 2], k=5) is equivalent to sample(['red', 'red', 'red', 'red', 'blue', 'blue'], k=5).
To choose a sample from a range of integers, use a :func:range object as an
argument. This is especially fast and space efficient for sampling from a large
population: sample(range(10000000), k=60).
If the sample size is larger than the population size, a :exc:ValueError
is raised.
.. versionchanged:: 3.9 Added the counts parameter.
.. versionchanged:: 3.11
The *population* must be a sequence. Automatic conversion of sets
to lists is no longer supported.
The following function generates a discrete distribution.
.. function:: binomialvariate(n=1, p=0.5)
Binomial distribution <https://mathworld.wolfram.com/BinomialDistribution.html>_.
Return the number of successes for n independent trials with the
probability of success in each trial being p:
Mathematically equivalent to::
sum(random() < p for i in range(n))
The number of trials n should be a non-negative integer.
The probability of success p should be between 0.0 <= p <= 1.0.
The result is an integer in the range 0 <= X <= n.
.. versionadded:: 3.12
.. _real-valued-distributions:
The following functions generate specific real-valued distributions. Function parameters are named after the corresponding variables in the distribution's equation, as used in common mathematical practice; most of these equations can be found in any statistics text.
.. function:: random()
Return the next random floating-point number in the range 0.0 <= X < 1.0
.. function:: uniform(a, b)
Return a random floating-point number N such that a <= N <= b for
a <= b and b <= N <= a for b < a.
The end-point value b may or may not be included in the range
depending on floating-point rounding in the expression
a + (b-a) * random().
.. function:: triangular(low, high, mode)
Return a random floating-point number N such that low <= N <= high and
with the specified mode between those bounds. The low and high bounds
default to zero and one. The mode argument defaults to the midpoint
between the bounds, giving a symmetric distribution.
.. function:: betavariate(alpha, beta)
Beta distribution. Conditions on the parameters are alpha > 0 and
beta > 0. Returned values range between 0 and 1.
.. function:: expovariate(lambd = 1.0)
Exponential distribution. lambd is 1.0 divided by the desired mean. It should be nonzero. (The parameter would be called "lambda", but that is a reserved word in Python.) Returned values range from 0 to positive infinity if lambd is positive, and from negative infinity to 0 if lambd is negative.
.. versionchanged:: 3.12
Added the default value for lambd.
.. function:: gammavariate(alpha, beta)
Gamma distribution. (Not the gamma function!) The shape and scale parameters, alpha and beta, must have positive values. (Calling conventions vary and some sources define 'beta' as the inverse of the scale).
The probability distribution function is::
x ** (alpha - 1) * math.exp(-x / beta)
pdf(x) = --------------------------------------
math.gamma(alpha) * beta ** alpha
.. function:: gauss(mu=0.0, sigma=1.0)
Normal distribution, also called the Gaussian distribution.
mu is the mean,
and sigma is the standard deviation. This is slightly faster than
the :func:normalvariate function defined below.
Multithreading note: When two threads call this function simultaneously, it is possible that they will receive the same return value. This can be avoided in three ways.
normalvariate function instead... versionchanged:: 3.11 mu and sigma now have default arguments.
.. function:: lognormvariate(mu, sigma)
Log normal distribution. If you take the natural logarithm of this distribution, you'll get a normal distribution with mean mu and standard deviation sigma. mu can have any value, and sigma must be greater than zero.
.. function:: normalvariate(mu=0.0, sigma=1.0)
Normal distribution. mu is the mean, and sigma is the standard deviation.
.. versionchanged:: 3.11 mu and sigma now have default arguments.
.. function:: vonmisesvariate(mu, kappa)
mu is the mean angle, expressed in radians between 0 and 2*\ pi, and kappa is the concentration parameter, which must be greater than or equal to zero. If kappa is equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2*\ pi.
.. function:: paretovariate(alpha)
Pareto distribution. alpha is the shape parameter.
.. function:: weibullvariate(alpha, beta)
Weibull distribution. alpha is the scale parameter and beta is the shape parameter.
.. class:: Random([seed])
Class that implements the default pseudo-random number generator used by the
:mod:!random module.
.. versionchanged:: 3.11
Formerly the seed could be any hashable object. Now it is limited to:
None, :class:int, :class:float, :class:str,
:class:bytes, or :class:bytearray.
Subclasses of :class:!Random should override the following methods if they
wish to make use of a different basic generator:
.. method:: Random.seed(a=None, version=2)
Override this method in subclasses to customise the :meth:`~random.seed`
behaviour of :class:`!Random` instances.
.. method:: Random.getstate()
Override this method in subclasses to customise the :meth:`~random.getstate`
behaviour of :class:`!Random` instances.
.. method:: Random.setstate(state)
Override this method in subclasses to customise the :meth:`~random.setstate`
behaviour of :class:`!Random` instances.
.. method:: Random.random()
Override this method in subclasses to customise the :meth:`~random.random`
behaviour of :class:`!Random` instances.
Optionally, a custom generator subclass can also supply the following method:
.. method:: Random.getrandbits(k)
Override this method in subclasses to customise the
:meth:`~random.getrandbits` behaviour of :class:`!Random` instances.
.. method:: Random.randbytes(n)
Override this method in subclasses to customise the
:meth:`~random.randbytes` behaviour of :class:`!Random` instances.
.. class:: SystemRandom([seed])
Class that uses the :func:os.urandom function for generating random numbers
from sources provided by the operating system. Not available on all systems.
Does not rely on software state, and sequences are not reproducible. Accordingly,
the :meth:seed method has no effect and is ignored.
The :meth:getstate and :meth:setstate methods raise
:exc:NotImplementedError if called.
Sometimes it is useful to be able to reproduce the sequences given by a pseudo-random number generator. By reusing a seed value, the same sequence should be reproducible from run to run as long as multiple threads are not running.
Most of the random module's algorithms and seeding functions are subject to change across Python versions, but two aspects are guaranteed not to change:
If a new seeding method is added, then a backward compatible seeder will be offered.
The generator's :meth:~Random.random method will continue to produce the same
sequence when the compatible seeder is given the same seed.
.. _random-examples:
Basic examples::
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]
Simulations::
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
Example of statistical bootstrapping <https://en.wikipedia.org/wiki/Bootstrapping_(statistics)>_ using resampling
with replacement to estimate a confidence interval for the mean of a sample::
from statistics import fmean as mean from random import choices
data = [41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95] means = sorted(mean(choices(data, k=len(data))) for i in range(100)) print(f'The sample mean of {mean(data):.1f} has a 90% confidence ' f'interval from {means[5]:.1f} to {means[94]:.1f}')
Example of a resampling permutation test <https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests>_
to determine the statistical significance or p-value <https://en.wikipedia.org/wiki/P-value>_ of an observed difference
between the effects of a drug versus a placebo::
# Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson
from statistics import fmean as 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 = 10_000
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.')
Simulation of arrival times and service deliveries for a multiserver queue::
from heapq import heapify, heapreplace
from random import expovariate, gauss
from statistics import mean, quantiles
average_arrival_interval = 5.6
average_service_time = 15.0
stdev_service_time = 3.5
num_servers = 3
waits = []
arrival_time = 0.0
servers = [0.0] * num_servers # time when each server becomes available
heapify(servers)
for i in range(1_000_000):
arrival_time += expovariate(1.0 / average_arrival_interval)
next_server_available = servers[0]
wait = max(0.0, next_server_available - arrival_time)
waits.append(wait)
service_duration = max(0.0, gauss(average_service_time, stdev_service_time))
service_completed = arrival_time + wait + service_duration
heapreplace(servers, service_completed)
print(f'Mean wait: {mean(waits):.1f} Max wait: {max(waits):.1f}')
print('Quartiles:', [round(q, 1) for q in quantiles(waits)])
.. seealso::
Statistics for Hackers <https://www.youtube.com/watch?v=Iq9DzN6mvYA>_
a video tutorial by
Jake Vanderplas <https://us.pycon.org/2016/speaker/profile/295/>_
on statistical analysis using just a few fundamental concepts
including simulation, sampling, shuffling, and cross-validation.
Economics Simulation <https://nbviewer.org/url/norvig.com/ipython/Economics.ipynb>_
a simulation of a marketplace by
Peter Norvig <https://norvig.com/bio.html>_ that shows effective
use of many of the tools and distributions provided by this module
(gauss, uniform, sample, betavariate, choice, triangular, and randrange).
A Concrete Introduction to Probability (using Python) <https://nbviewer.org/url/norvig.com/ipython/Probability.ipynb>_
a tutorial by Peter Norvig <https://norvig.com/bio.html>_ covering
the basics of probability theory, how to write simulations, and
how to perform data analysis using Python.
These recipes show how to efficiently make random selections
from the combinatoric iterators in the :mod:itertools module
or the :pypi:more-itertools project:
.. testcode::
import random
def random_product(*iterables, repeat=1): "Random selection from itertools.product(*iterables, repeat=repeat)" pools = tuple(map(tuple, iterables)) * repeat return tuple(map(random.choice, pools))
def random_permutation(iterable, r=None): "Random selection from itertools.permutations(iterable, r)" pool = tuple(iterable) r = len(pool) if r is None else r return tuple(random.sample(pool, r))
def random_combination(iterable, r): "Random selection from itertools.combinations(iterable, r)" pool = tuple(iterable) n = len(pool) indices = sorted(random.sample(range(n), r)) return tuple(pool[i] for i in indices)
def random_combination_with_replacement(iterable, r): "Choose r elements with replacement. Order the result to match the iterable." # Result will be in set(itertools.combinations_with_replacement(iterable, r)). pool = tuple(iterable) n = len(pool) indices = sorted(random.choices(range(n), k=r)) return tuple(pool[i] for i in indices)
def random_derangement(iterable): "Choose a permutation where no element stays in its original position." seq = tuple(iterable) if len(seq) < 2: if not seq: return () raise IndexError('No derangments to choose from') perm = list(range(len(seq))) start = tuple(perm) while True: random.shuffle(perm) if all(p != q for p, q in zip(start, perm)): return tuple([seq[i] for i in perm])
.. doctest:: :hide:
>>> import random
>>> random.seed(8675309)
>>> random_product('ABCDEFG', repeat=5)
('D', 'B', 'E', 'F', 'E')
>>> random.seed(8675309)
>>> random_permutation('ABCDEFG')
('D', 'B', 'E', 'C', 'G', 'A', 'F')
>>> random_permutation('ABCDEFG', 5)
('A', 'G', 'D', 'C', 'B')
>>> random.seed(8675309)
>>> random_combination('ABCDEFG', 7)
('A', 'B', 'C', 'D', 'E', 'F', 'G')
>>> random_combination('ABCDEFG', 6)
('A', 'B', 'C', 'D', 'F', 'G')
>>> random_combination('ABCDEFG', 5)
('A', 'B', 'C', 'E', 'F')
>>> random_combination('ABCDEFG', 4)
('B', 'C', 'D', 'G')
>>> random_combination('ABCDEFG', 3)
('B', 'E', 'G')
>>> random_combination('ABCDEFG', 2)
('E', 'G')
>>> random_combination('ABCDEFG', 1)
('C',)
>>> random_combination('ABCDEFG', 0)
()
>>> random.seed(8675309)
>>> random_combination_with_replacement('ABCDEFG', 7)
('B', 'C', 'D', 'E', 'E', 'E', 'G')
>>> random_combination_with_replacement('ABCDEFG', 3)
('A', 'B', 'E')
>>> random_combination_with_replacement('ABCDEFG', 2)
('A', 'G')
>>> random_combination_with_replacement('ABCDEFG', 1)
('E',)
>>> random_combination_with_replacement('ABCDEFG', 0)
()
>>> random.seed(8675309)
>>> random_derangement('')
()
>>> random_derangement('A')
Traceback (most recent call last):
...
IndexError: No derangments to choose from
>>> random_derangement('AB')
('B', 'A')
>>> random_derangement('ABC')
('C', 'A', 'B')
>>> random_derangement('ABCD')
('B', 'A', 'D', 'C')
>>> random_derangement('ABCDE')
('B', 'C', 'A', 'E', 'D')
>>> # Identical inputs treated as distinct
>>> identical = 20
>>> random_derangement((10, identical, 30, identical))
(20, 30, 10, 20)
The default :func:.random returns multiples of 2⁻⁵³ in the range
0.0 ≤ x < 1.0. All such numbers are evenly spaced and are exactly
representable as Python floats. However, many other representable
floats in that interval are not possible selections. For example,
0.05954861408025609 isn't an integer multiple of 2⁻⁵³.
The following recipe takes a different approach. All floats in the interval are possible selections. The mantissa comes from a uniform distribution of integers in the range 2⁵² ≤ mantissa < 2⁵³. The exponent comes from a geometric distribution where exponents smaller than -53 occur half as often as the next larger exponent.
::
from random import Random
from math import ldexp
class FullRandom(Random):
def random(self):
mantissa = 0x10_0000_0000_0000 | self.getrandbits(52)
exponent = -53
x = 0
while not x:
x = self.getrandbits(32)
exponent += x.bit_length() - 32
return ldexp(mantissa, exponent)
All :ref:real valued distributions <real-valued-distributions>
in the class will use the new method::
>>> fr = FullRandom()
>>> fr.random()
0.05954861408025609
>>> fr.expovariate(0.25)
8.87925541791544
The recipe is conceptually equivalent to an algorithm that chooses from
all the multiples of 2⁻¹⁰⁷⁴ in the range 0.0 ≤ x < 1.0. All such
numbers are evenly spaced, but most have to be rounded down to the
nearest representable Python float. (The value 2⁻¹⁰⁷⁴ is the smallest
positive unnormalized float and is equal to math.ulp(0.0).)
.. seealso::
Generating Pseudo-random Floating-Point Values <https://allendowney.com/research/rand/downey07randfloat.pdf>_ a
paper by Allen B. Downey describing ways to generate more
fine-grained floats than normally generated by :func:.random.
.. _random-cli:
.. versionadded:: 3.13
The :mod:!random module can be executed from the command line.
.. code-block:: sh
python -m random [-h] [-c CHOICE [CHOICE ...] | -i N | -f N] [input ...]
The following options are accepted:
.. program:: random
.. option:: -h, --help
Show the help message and exit.
.. option:: -c CHOICE [CHOICE ...] --choice CHOICE [CHOICE ...]
Print a random choice, using :meth:choice.
.. option:: -i <N> --integer <N>
Print a random integer between 1 and N inclusive, using :meth:randint.
.. option:: -f <N> --float <N>
Print a random floating-point number between 0 and N inclusive,
using :meth:uniform.
If no options are given, the output depends on the input:
--choice.--integer.--float... _random-cli-example:
Here are some examples of the :mod:!random command-line interface:
.. code-block:: console
$ # Choose one at random $ python -m random egg bacon sausage spam "Lobster Thermidor aux crevettes with a Mornay sauce" Lobster Thermidor aux crevettes with a Mornay sauce
$ # Random integer $ python -m random 6 6
$ # Random floating-point number $ python -m random 1.8 1.7080016272295635
$ # With explicit arguments $ python -m random --choice egg bacon sausage spam "Lobster Thermidor aux crevettes with a Mornay sauce" egg
$ python -m random --integer 6 3
$ python -m random --float 1.8 1.5666339105010318
$ python -m random --integer 6 5
$ python -m random --float 6 3.1942323316565915