I hope this is appropriate for this section

Recently, I was asked to find the probability density function of distribution (pdf) of tossing 20 coins at a time. The time it took me to write a Monte Carlo simulation was half the time it took me to compute it from the binomial dist or by building a Pascal's triangle. Maybe thats not a good reflection on my math, but as you will see, I'm not a fancy Perl programmer either :)

Anyway, here is the code which produces very accurate results in a matter of 30sec on my modest laptop.

I added mind numbing comments for utter beginners. Enjoy !

Regards, James

# coinToss.pl
#
# Toss a collection (20 in this example) of coins a large number of ti
+mes
# to determine the distribution of Heads and Tails.
# N.B. P(Head) = P(Tail) = 50% = 0.5

use strict;

# Inputs
my $numTosses = 20;        # The num of coin tosses per experiment (20
+ in this example)
my $runs = 10000000;    # 10 Million - the num of times we repeat the 
+experiment

# Program vars
my $i;            # a looping variable
my $j;            # another looping var
my $toss;        # Keeps running total of the number of 'Heads' during
+ current experiment
my @collect;    # An array that keeps a total of the number of 'Heads'
+ counted 
                # in all previous experiment.
my $percent;    # To convert $collect[0] - $collect[19] to % 

# Outer loop: Repeat "$runs" times 
for ($j = 0; $j < $runs; $j++) {
    # Inner loop: One run of 20 tosses
    for ($i = 0; $i < $numTosses; $i++) {
        $toss += (rand() < 0.5) ? 1 : 0;
        #print "$toss\n";
    }
    $collect[$toss]++;
    $toss = 0;
}

# Print results
print "\nTails\tCount out of $runs\t%\n";
for ($i = 0; $i < $numTosses+1; $i++) {
    $percent = sprintf "%.2f", $collect[$i] / $runs * 100;
    print "$i\t$collect[$i]\t\t\t$percent%\n"
}
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