Question

3. Use Matlab to check that if X is a Beta-(a,b) random variable with a = b = į and if, conditional on this Y1, Y2 are independent Bernoulli-p random variables for p = X, and we find Yi + Y2 = k = 1 (so that 2 - Y1 - Y2 is also 1), then the conditional distributrion of X is Beta-(a', b') for a' = b' = 3. My plot (for the number of trials equal to 100,000) is as follows: Figure File View it Tools Desktop Window 300 200 150 100 50 0.2 04 0.6 08 1

Answer 1

for jj = 1 : 100

a = 1/2;
b = 1/2;
n = 100;
% Suppose X is beta-(a, b)
X = betarnd(a, b);
p = X;

Y1 = binornd(1, p.*ones(n,1));
Y2 = binornd(1, p.*ones(n,1));

k = Y1+Y2;
a_dash = 3/2;
b_dash = 3/2;
N = n;
z = 0;
Ane = zeros(n+1,1);
Ane(1) = 0;
res = zeros(jj,1);
for ii = 1:1:(N)
if k(ii) == 1

X = betarnd(a_dash, b_dash);
z = X;
Ane(ii+1) = z + Ane(ii) ;
%Y1 = binornd(1, p.*ones(n,1));
%Y2 = binornd(1, p.*ones(n,1));

end
end

res(jj) = Ane(n+1)

plot(res)
hold on
end