Just curious if anyone knows why there is a tiny but definite difference between the standard deviation as calculated by the error propagation formula and the simulation. It is only a 0.2% difference and doesn't cause me any problems personally but I am curious which of the two would be considered more accurate?
Adding another zero to the rnorm function causes my computer to crash. But I repeated this code 10 times or so (very small variance) and I am confident that the mean is in fact 0.2% higher than it should be.
# This takes about 6 seconds to run x <- rnorm(10000000,mean = 100, sd = 10) y <- rnorm(10000000,mean = 100, sd = 10) z <- x*y # SD of x*y using simulation sd(z) # SD of x*y using formula (((10/100)^2+(10/100)^2)^.5)*(100*100)