Computing many probabilities without a for loop

Hi, I have N X 2 matrix, mu, and N X 3 matrix, SIGMA, where mu(i,:) is a row vector of expectations for i-th bivariate normal distribution and SIGMA(i,:) is a row vector of elements of the covariance matrix for i-th bivariate normal distribution, i.e.,

[SIGMA(i,1) SIGMA(i,2); SIGMA(i,2) SIGMA(i,3)] is the covariance matrix of for i-th bivariate normal distribution,

and there are N bivariate normal distribution. For each i, I want to compute the probability of each bivariate normal random variable being positive, i.e.,

for i=1:N Y(i) = mvncdf([0 0],[Inf Inf],mu(i,2:3),[SIGMA(i,1) SIGMA(i,2); SIGMA(i,2) SIGMA(i,3)]); end

Is there any way to do this without the for loop? I have a large N and I want to circumvent using the for loop. I'd really appreciate your guidance. Thank you very much in advance!

Best, John