
175Simulation Methods in Engineering Design
when one only has access to a scientic calculator. Even when using a sci-
entic programming platform with access to the inverse CDF function, the
Box–Muller method is preferred because it is much faster. Using two uni-
form seeds, u
1
and u
2
, we get
=− π2lncos 2
2
zuu (6.8)
=− π2lnsin 2
2
u (6.9)
Example 6.4
Using the first and second column seeds in Example 6.2 generate 10 realiza-
tions of two independent standard normal random variables.
Solution
Using the Equations 6.8 and 6.9 we get the variables shown in Table6.5.
Notice that the means and standard deviations of Z
1
and Z
2
will approach 0
and 1 for ...