use strict;
    use warnings;
    
    use Statistics::Descriptive;
    
    my $n_simulations   = 1000;
    my $circumference   = 1000;
    my @lengths_distrib = (100) x 100;    # distibution of range lengths
    my $some_pos        = 36;             # arbitrary position
    
    my $stat = Statistics::Descriptive::Full->new();
    
    foreach my $sim ( 1 .. $n_simulations ) {
    
    	# randomly map ranges onto circumference
    	
    	my @random_ranges =
    		map { my $start = int( rand($circumference) ); [ $start, ( $start + $_ -1 ) % $circumference ] }
    		@lengths_distrib;
    	
    	# count how many range contain $some_pos
    	my $num_covering_ranges = scalar(
    		grep { ( $_->[0] <= $some_pos and $_->[1] >= $some_pos ) or ( $_->[1] < $_->[0] and $_->[1] > $some_pos ) }
    			@random_ranges
    	);
    	$stat->add_data($num_covering_ranges);
    }
    print $stat->mean, ' ', $stat->variance, "\n";