Simulation Variables

Basis RVs

$X\left({\mu }_i,{\sigma }_i\right)$

$R_1\left(3,0.7\right)$

$R_2\left(5,1.0\right)$

$H\left(20,2.0\right)$

$C\left(1,0.2\right)$

Composite RVs

$Z=\left(\text{π}/3\right)\left(R_1^2+R_1{R}_2+R_2^2\right)HC$

$Y=\ln \left(Z\right)$

Mean

$\overline{Z}$ or $\langle Z\rangle$

S.E.

$S_Z$ or ${\Sigma }_Z$

Mean

$\overline{Y}$ or $\langle Y\rangle$

S.D.

$s_Y$ or ${\sigma }_Y$

S.E.

$S_Y$ or ${\Sigma }_Y$

Sample

n = 1706

982

38.56

6.57

0.72

0.017

Simulation

Log-Normal

n = 1,000,000

1057

0.42

6.89

0.38

0.00038

Theoretical Expectations

1057

0.41

6.89

0.38

0.00038

Simulation

Normal

n = 1,000,000

1057

0.40

6.89

0.39

0.00039

Theoretical Expectations

1061

0.43

6.89

0.39

0.00039

True Count

1111