How to generate multivariate normal data in R?

I'm completing an assignment, in which I have to generate a sample X = (X1, X2) from a bivariate normal in which each marginal is N(0,1) and the correlation between X1 and X2 is 0.5. I think the way to approach this is to use the mvrnorm function, but I'm not quite sure how to proceed after that. Any advice? Thanks in advance!

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3 Answers 3

Indeed, the mvrnorm function from the MASS package is probably your best bet. This function can generate pseudo-random data from multivariate normal distributions.

Examining the help page for this function ( ??mvrnorm ) shows that there are three key arguments that you would need to simulate your data based your given parameters, ie:

n - the number of samples required (an integer);
mu - a vector giving the means of the variables - here, your distributions are standard normal so it will be a vector of zeros; and
Sigma - a positive-definite symmetric matrix specifying the covariance matrix of the variables - ie, in your case, a matrix with variance on the diagonal of ones and covariance on the off-diagonals of 0.5.

Have a look at the examples in this help page, which should help you put these ideas together!