Bivariate in R (mvtnorm package)

Question

I have two normal r.v.\'s that are independent of each other (so the correlation $\\rho= 0$). The two r.v.\'s come from the following two Normal distributions, i.e., $X\\sim N

Answer 1

You were forgetting to include the variance of your random variables. Instead of specifying the correlation matrix, just specify the covariance matrix. Here is the R code to do it:

library(mvtnorm)

   mu = c(18,12.72)
   covariance = diag(c(5.7,30.38),2)
   X = c(10,-Inf)
   Y = c(Inf,10)

   pmvnorm(mean=mu,sigma=covariance,lower=X,upper=Y)