Mean (Monte Carlo Simulation)

Mean (Theory

Equation (20))

Std. Dev. (Monte Carlo Simulation)

Std. Dev. (Theory Equation (23))

t = 10

x

−0.0123

3.2095

y

−0.0080

3.2205

z

0.0389

3.2338

Average

0.0062

0.0

3.2213

3.0848

r

5.0802

4.8830

2.3070

2.1692

t = 50

x

−0.0345

6.2989

y

−0.0209

6.3027

z

0.0225

6.3196

Average

−0.0110

0.0

6.3071

6.2727

r

9.6762

9.6547

5.0705

4.9828

t = 100

x

0.0215

7.9626

y

0.0259

7.9500

z

−0.0037

7.9225

Average

0.0146

0.0

7.9450

7.9506

r

11.8653

11.9176

6.9704

6.8998

t = 1000

x

0.0122

9.9410

y

−0.0252

9.9394

z

−0.0035

9.9085

Average

−0.0055

0.0

9.9296

9.9998

r

14.0043

14.1421

9.9835

9.9995