function pdf = birthday_pdf ( n )
%*****************************************************************************80
%
%% birthday_pdf() returns the Birthday Concurrence PDF.
%
% Discussion:
%
% The probability is the probability that the N-th person is the
% first one to match a birthday with someone earlier.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 26 August 2006
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer N, the number of people whose birthdays have been
% disclosed.
%
% Output:
%
% real PDF, the probability that the N-th person
% is the first to match a birthday with someone earlier.
%
if ( n < 1 || 365 < n )
pdf = 0.0;
return
end
pdf = 1.0;
%
% Compute the probability that the first N-1 people have distinct birthdays.
%
for i = 1 : n - 1
pdf = pdf * ( 365 + 1 - i ) / 365.0;
end
%
% Compute the probability that person N has one of those N-1 birthdays.
%
pdf = pdf * ( n - 1 ) / 365.0;
return
end