Simulation Variables

Basis RVs

X ( μ i , σ i )

R 1 ( 3 , 0.7 )

R 2 ( 5 , 1.0 )

H ( 20 , 2.0 )

C ( 1 , 0.2 )

Composite RVs

Z = ( π / 3 ) ( R 1 2 + R 1 R 2 + R 2 2 ) H C

Y = ln ( Z )

Mean

Z ¯ or Z

S.E.

S Z or Σ Z

Mean

Y ¯ or Y

S.D.

s Y or σ Y

S.E.

S Y or Σ 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