$d$

$Y_t$

$E\left(Y_t\right)={\mu }_{Y_t}$

$\mathrm{var}\left(Y_t\right)={\sigma }_{Y_t}^2$

${\sigma }_{Y_t}\text{when}\sigma =1.0$

1

$X_t$

0

${\sigma }^2$

1.0000

2

$X_t^2$

${\sigma }^2$

$2{\sigma }^4$

1.4142

3

$X_t^3$

0

$15{\sigma }^6$

3.8730

4

$X_t^4$

$3{\sigma }^4$

$96{\sigma }^8$

9.7980

5

$X_t^5$

0

$945{\sigma }^{10}$

30.7409

6

$X_t^6$

$15{\sigma }^6$

$10170{\sigma }^{12}$

100.8464

7

$X_t^7$

0

$135135{\sigma }^{14}$

367.6071

8

$X_t^8$

$105{\sigma }^8$

$2016000{\sigma }^{16}$

1419.8591

9

$X_t^9$

0

$34459425{\sigma }^{18}$

5870.2151

10

$X_t^{10}$

$10395{\sigma }^{10}$

$653836050{\sigma }^{20}$

25570.2180