Timeline for Derivatives through random variables?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 19, 2016 at 23:08 | comment | added | Charlie Parker | now that Im re-reading the question I think I misunderstood it. It seems that the issue was that he couldn't take the derivative of of x, of course if x is an observed sample its a fixed number so taking a derivative of it leads to 0. It seems that taking the derivative of $\theta$ remains sensible even with samples observed (i.e. its similar to MLE, maximum likelihood estimation). | |
| Aug 19, 2016 at 22:59 | comment | added | BSteinhurst | @Pinocchio because you did not take the derivative of little x as a function of theta but rather of the probability that big X = 1 as a function of theta. | |
| Aug 19, 2016 at 2:12 | comment | added | Charlie Parker | I read your answer but I didn't understand it. Why is my counter example wrong. Consider $P_{\theta}(X = x) = \theta^x (1 - \theta)^{1-x}$ and let $x=1$ be the sample observed. Then $P_{\theta}(X = 1) = \theta $. One can easily take the derivative of that function, it has $\theta$ as a variable, its derivative is simply 1. Why is that not correct? | |
| Oct 18, 2012 at 16:49 | vote | accept | Ian Goodfellow | ||
| Oct 17, 2012 at 18:20 | history | answered | BSteinhurst | CC BY-SA 3.0 |