% 
% Written by:
% -- 
% John L. Weatherwax                2007-09-10
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; drawnow; 
clc; clear; 

pC = @(x) poisspdf( x, 4 );
pT = @(x) poisspdf( x, 2 );

% Part (a): 
%
num = pC( 4 ) * pT( 0 );
p_c_p_t_4 = sum( pC( 4:-1:0 ) .* pT( 0:4 ) ); % this is P\{ C+T=4 \} 
num/p_c_p_t_4

% Using the binomial conditional density:
(2/3)^4 

% Part (b): 
%
num = sum( (0:4) .* pC( 0:4 ) .* pT( 4:-1:0 ) );
num/p_c_p_t_4

% Using the binomial conditional density:
8/3