Timeline for Representing a conditional expectation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 31 at 11:23 | history | edited | Speltzu | CC BY-SA 4.0 |
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| May 31 at 11:05 | history | edited | Speltzu | CC BY-SA 4.0 |
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| May 31 at 10:54 | history | edited | Speltzu | CC BY-SA 4.0 |
added 1861 characters in body
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| May 30 at 6:02 | comment | added | Speltzu | $E[X\mid\sigma(X>c)]$ is necessarily of the form $A1_{X>c}+B1_{X\leq c}$. We call $E[X\mid X>c]$ and $E[X\mid X\leq c]$ the constants $A$ and $B$. Similarly $P[X\in A\mid\sigma(X>c)]=P[X\in A\mid X>c]1_{X>c}+P[X\in A\mid X\leq c ]1_{X\leq c}$. Certainly the conditional expectations are integral with respect to these conditional probabilities. | |
| May 30 at 3:35 | comment | added | msantama | If you meant to write $\mathbf{E}\left( X \mid \sigma \left( X > c \right) \right) = \mathbf{E}\left( X \mid \sigma \left( X > c \right) \right) \mathbf{1}_{X > c} + \mathbf{E}\left( X \mid \sigma \left( X \leq c \right) \right) \mathbf{1}_{X \leq c}$ then I certainly agree. But then $\mathbf{E}\left( \mathbf{E}\left( X \mid \sigma \left( X > c \right) \right) \mathbf{1}_{X > c} \right) = \mathbf{E}\left( \mathbf{E}\left( X \mid X > c \right) \mathbf{1}_{X > c} \right)$ does not follow. | |
| May 30 at 3:25 | comment | added | msantama | I'm not sure I follow. What is the definition of $\mathbf{E}\left( X \mid X > c \right)$ you use? Your first line suggests the definition is $\frac{\mathbf{E}\left( X \mid \sigma \left( X > c \right) \right) - \mathbf{E}\left( X \mid X \leq c \right) \mathbf{1}_{X \leq c}}{\mathbf{1}_{X > c}}$ | |
| May 29 at 16:00 | history | answered | Speltzu | CC BY-SA 4.0 |