Exercise - Simulating the Bivariate Normal Distribution
Write an R function called rbinorm()
that uses rnorm()
to generate draws from a bivariate, i.e. two-dimensional, normal distribution. Your function should take three arguments: n_draws
is the number of simulation draws, mean_vec
is a vector of length two specifying the mean of each component, and var_mat
is a \((2\times 2)\) variance-covariance matrix. Read the documentation for the R function stopifnot()
and use it to throw an error if var
is not positive definite. Your function should return an nreps
by 2
matrix containing the desired draws. You may not use function chol()
: I want you to do everything “by hand.” Check your work by drawing a large number of simulations, calculating the sample means and variance-covariance matrices, and plotting the marginal and joint distribution.