function [] = chap_4_prob_15()
% 
% Written by:
% -- 
% John L. Weatherwax                2007-04-02
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; 

% compute P{X=1}: 
% 
P_X_1 = 11/66

% compute P{X=2}: 
% 
k = 2:11;
pt1 = (12 - k)/66;
pt2 = 11./(54+k);
P_X_2 = sum( pt1.*pt2 )

% compute P{X=3}: 
% 
P_X_3 = 0.0;
for k=2:11,
  jvals = [ 2:(k-1), (k+1):11 ]; % the j indices without the index k 
  pt1 = (12 - jvals)/66;
  pt2 = (12 - k)./(54 + jvals);
  pt3 = 11./(42+jvals+k);
  P_X_3 = P_X_3 + sum( pt1 .* pt2 .* pt3 );
end
P_X_3

P_X_4 = 1 - P_X_1 - P_X_2 - P_X_3