class Population
{ 
        has @.population;

        method BUILD() {
                .population = <>;
        }

        method add($x) {
                push(.population, $x);
        }

}

##</code><code>##

use Population;

class DistributionPopulation is Population
{
        method BUILD() {

        }

        method Expectance() {

                my $e = 0.0;

                for .population -> $p {
                        $e += $p;
                }

                return $e / .population.length;
        }

        method Variance () {
                my $e = .Expectance();
                my $var = 0.0;

                for .population -> $p {
                        $var += ($p - $e) * ($p - $e);
                }

                return $var / (.population.length - 1);
        }


}

##</code><code>##

class Covariance {
  
        method Covariance($xpop,$ypop) {
                my $ex = $xpop.Expectance();
                my $ey = $ypop.Expectance();

                my $cov = 0.0;

                for $xpop.population, $ypop.population -> $p,$q {
                        $cov += ($p - $ex)  * ($q - $ey);
                }

                return $cov / $xpop.population.length;

        }
}

##</code><code>##

use Covariance;
  
role ThisCovariance { method cov($xpop,$ypop) {
        return Covariance().Covariance($xpop,$ypop);
}
}


class Correlation does ThisCovariance {
        method BUILD() {

        }

        method correlation($xpop,$ypop) { ### These are distribution args

                my $varx = $xpop.Variance(), $vary = $ypop.Variance();
                my $cov = .cov($xpop, $ypop);

                return $cov / (sqrt($varx) * sqrt($vary));

        }
}