.. _random-numbers-checking-the-other-values:

Checking the other values
-------------------------

``how_many`` only counts the occurrences of a particular value, and we
are interested in seeing how many times each value appears. We can solve
that problem with a loop:

::

     std::size_t num_values = 20;
     int upper_bound = 9;
     std::vector<int> numbers = make_vector (num_values, upper_bound);

     std::cout << "value\thow_many";

     for (int i = 0; i<=upper_bound; ++i) {
       std::cout << i << '\t' << how_many (numbers, i) << '\n';
     }

Notice that it is legal to declare a variable inside a ``for``
statement. This syntax is sometimes convenient, but you should be aware
that a variable declared inside a loop only exists inside the loop. If
you try to refer to ``i`` later, you will get a compiler error.

This code uses the loop variable as an argument to ``how_many``, in order
to check each value between 0 and 9, in order. The result is:

::

   value   how_many
   0       2
   1       1
   2       3
   3       3
   4       0
   5       2
   6       5
   7       2
   8       0
   9       2

Again, it is hard to tell if the digits are really appearing equally often. 
If we increase ``num_values`` to 100,000 we get the following:

::

   value   how_many
   0       10130
   1       10072
   2       9990
   3       9842
   4       10174
   5       9930
   6       10059
   7       9954
   8       9891
   9       9958

In each case, the number of appearances is within about 1% of the
expected value (10,000), so we conclude that the random numbers are
probably uniform.

.. tb-group::
   :name: self_check

   .. tb-tab:: Q1

      .. tb-choice::
         :name: checking_values_1

         If you declare a variable inside a ``for`` statement, where can it exist?

         - [x] inside of the for loop.

           Correct!
         - [ ] outside of the for loop, but inside of the function it's used in.

           Incorrect! The variable goes out of scope as soon as the for loop terminates!
         - [ ] outside of the function, and everywhere else in the program.

           Incorrect! The variable goes out of scope as soon as the for loop terminates!

   .. tb-tab:: Q2

      .. tb-choice::
         :name: checking_values_2

         **Multiple Response** When we increase the size of ``num_values``, which of the following is true:

         - [x] the difference between actual and expected number of appearances increases

           Correct! The numbers go from being off by less than 5 to more than 100.
         - [ ] the difference between actual and expected number of appearances decreases

           Incorrect! Take a look at the numbers again!
         - [ ] the percent by which the number of appearances differs from the expected number increases

           Incorrect! Take a look at the numbers again!
         - [x] the percent by which the number of appearances differs from the expected number decreases

           Incorrect! As we continue to increase the size of num_values, the percent by which the number of appearances differes from the expected value approaches 0.