.. _random-numbers-statistics:

Statistics
----------

The numbers generated by ``random`` are frequently distributed
uniformly. That means that each value in the range should be equally
likely. If we count the number of times each value appears, it should be
roughly the same for all values, provided that we generate a large
number of values.

In the next few sections, we will write programs that generate a
sequence of random numbers and check whether this property holds true.

Although the :numeric:`uniform int distribution <random/uniform_int_distribution>`
is both common and often desired, the C++ random library defines several other
distributions useful in science and engineering, including:

- :numeric:`bernoulli distribution <random/bernoulli_distribution>`
- :numeric:`binomial distribution <random/binomial_distribution>`
- :numeric:`poisson distribution <random/poisson_distribution>`
- :numeric:`normal distribution <random/normal_distribution>`

and others that are part of these broad families of distributions.

The convenience and ease of use of these and other functions in the C++
random library is one of many excellent reasons to use them instead of the
``rand()`` family of functions they replace from the C library.

.. tb-group::
   :name: self_check

   .. tb-tab:: Q1

      .. tb-blank::
         :name: statistics_1

         Random numbers are frequently distributed __________.

         {{blank}}

         .. tb-answer::
            :regex:
            :match: uniformly
            :feedback: Correct!
            :incorrect: Incorrect!