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			<title>Probability estimate using Monte Carlo methods</title>
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			<h1>Probability estimate using Monte Carlo methods</h1>
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			<span class="keyword">function</span> prob = montecarlo(A,b,Sigma,notrials);

			<span class="comment">% Estimates the probability that a random vector x in R2</span>
			<span class="comment">% with mean zero and covariance Sigma satisfies Ax <= b,</span>
			<span class="comment">% based on 100 * notrials trials. Sigma must be PSD.</span>

			m = size(A,1);

			R = chol(Sigma); <span class="comment">% Y = R^{-T}X has covariance I</span>
			X = R'*randn(2,notrials);
			prob = length(find(sum(A*X - b(:,ones(1,notrials)) < 0) == m))/notrials;

			<span class="keyword">for</span> i=1:99
			X = R'*randn(2,notrials);
			prob = 0.5*(prob + <span class="keyword">...</span>
			length(find(sum(A*X - b(:,ones(1,notrials)) < 0) == m))/notrials);
			<span class="keyword">end</span>;
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