%% Section 7.1
%% Computing the convolution of two vectors
% The MATLAB command *conv* lets you compute the convolution of two
% vectors. So, for example, if u, v are given by
u = [1/4 1/4 1/2]
v = [1/9 2/9 1/9 1/3 1/18 1/6]
%%
% their convolution is 
conv(u,v)
%% Rolling a die 10 times
% Suppose you are interested in the distribution that results from rolling
% a die 10 times. The distribution for rolling once is:
w = [1/6 1/6 1/6 1/6 1/6 1/6]
%%
% The distribution for the sum is the convolution of w with itself 9 times.
% Here's a way to compute it.
p = w; % initialize p. 
for j = 1:9
    p = conv(p,w); % p is the result of convolving w with itself j times
end
%% 
% The resulting distribution is:
p
%%
% A good way to make sense of this is to view it as a bar graph. Now 
% the values of p range from 10 to 60. 
bar(10:60,p)
axis([10 60 0 0.08])