# Discrepancy between calculated and simulated error propagation

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)

• yeah i read the formula is an approximation. So would the simulation be more accurate then? – John Mar 10 '13 at 18:11