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Mar
22
answered How do you filter through published papers and find the ones you should read?
Mar
22
answered Do non-mathematical fields use the appropriate level of analytic/probabilistic rigor?
Mar
21
revised Combining independent probabilities of an event
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Mar
21
answered Combining independent probabilities of an event
Mar
21
answered Conditional Probability Problem (drawing chips from an urn)
Mar
20
comment How to estimate the number of articles on Wikipedia using the “random article” function?
This seems like a good problem for a latent random graph model. Given a model of some graph parameters (which will control the number of nodes and the diameter, etc.), you could use some Bayesian model fitting methods to decide which graph likely gives rise to your observed number of pages-before-repeat. That is how I would start, at least. Unlike the German tank problem, this one is sensitive to the graph structure you assume. There are well-confirmed network models of wiki-like graphs, though. Check out M.E.J. Newman's recent book on networks for some examples.
Mar
20
comment probability of sequential events
Note that it can fail either right away at point 1 (you know the probability of that) or (with probability that it does not fail at point 1) it can fail at point 2 with a probability that you know. Add these to get total probability of failure, F, then 1-F is the probability of success.
Mar
20
answered Is it possible to prove that a problem $P$ is decidable in $O(\phi)$ without providing an algorithm that decides $P$ in $O(\phi)$?
Mar
20
revised General properties of eigenvalues of a Jacobian matrix when premultiplied by a symmetric, positive definite matrix?
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Mar
20
asked General properties of eigenvalues of a Jacobian matrix when premultiplied by a symmetric, positive definite matrix?
Mar
20
revised How to find the conditional expectation for this pdf
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Mar
20
comment How to find the conditional expectation for this pdf
You're right. The mistake though is not quite what you mentioned. It is that in my first conditional expectation, I forgot to divide by the marginal probability $P(X_{1} = x_{1})$. Then, multiplying by that again will cancel it to make the last formula correct. I am updating to reflect this.
Mar
20
comment How to find the conditional expectation for this pdf
But the first term of the product is just for a single value of $x_{1}$. You have to multiply by the probability of that value of $x_{1}$ and sum over all potential choices for $x_{1}$.
Mar
20
answered How to find the conditional expectation for this pdf
Mar
19
answered How can I calculate the CDF of this random variable?
Mar
19
comment proving gradient of a scalar field is perpendicular to equipotential surface
These MIT notes mention the integral definition, but the directional derivative one that you mention is just as good. @Bruno -- fixed the typo, thanks!
Mar
19
revised proving gradient of a scalar field is perpendicular to equipotential surface
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Mar
19
answered Binary random variables event-level independence implies random variable independence
Mar
19
revised proving gradient of a scalar field is perpendicular to equipotential surface
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Mar
19
answered proving gradient of a scalar field is perpendicular to equipotential surface