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| Both sides previous revision Previous revision Next revision | Previous revision | ||
| 진화생물학:가지치기_과정 [2016/07/20 21:03] – [푸아송 분포] minjae | 진화생물학:가지치기_과정 [2023/09/05 15:46] (current) – external edit 127.0.0.1 | ||
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| \phi_{X_{n}} &=& E[s^{X_{n}}] \\ | \phi_{X_{n}} &=& E[s^{X_{n}}] \\ | ||
| &=& \sum_{k=0}^{\infty} E[s^{X_{n}} | X_{n-1} = k] P(X_{n-1} = k) \\ | &=& \sum_{k=0}^{\infty} E[s^{X_{n}} | X_{n-1} = k] P(X_{n-1} = k) \\ | ||
| - | &=& \sum_{k=0}^{\infty} E[s^{W_{1}+W_{2}+...+W_{k}] P(X_{n-1} = k)\\ | + | &=& \sum_{k=0}^{\infty} E[s^{W_{1}+W_{2}+...+W_{k}}] P(X_{n-1} = k)\\ |
| - | &=& \sum_{k=0}^{\infty} E(s^{W_{1}} E(s^{W_{1}}) \ldots E(s^{W_{k}}) P(X_{n-1} = k)\\ | + | &=& \sum_{k=0}^{\infty} E(s^{W_{1}}) E(s^{W_{1}}) \ldots E(s^{W_{k}}) P(X_{n-1} = k)\\ |
| &=& \sum_{k=0}^{\infty} \phi(s)^{k} P(X_{n-1} = k) \\ | &=& \sum_{k=0}^{\infty} \phi(s)^{k} P(X_{n-1} = k) \\ | ||
| &=& \phi_{X_{n-1}}(\phi(s)) | &=& \phi_{X_{n-1}}(\phi(s)) | ||