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?- love(math) is unrequited. true.


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
Mar
19
revised what is the intuition behind Delta method?
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Mar
19
answered what is the intuition behind Delta method?
Mar
19
comment what is the intuition behind Delta method?
$f(x) = x(1-x)$, so $f(\mu) = \mu(1-\mu)$. Just follow the exact procedure as in this example, but substituting in the properties of your distribution and your function.
Mar
19
comment what is the intuition behind Delta method?
You're very close to getting it. First, just plug $\mu$ directly into the formula for $f(x) = x(1-x)$. Think about what the function applied to the mean value is (it's not $k\theta$). Secondly, you are correct to think of the CLT for the approximate distribution of $\bar{X}_{n}$.. but why would it have mean $0$? It won't converge to a standard normal unless you subtract the mean and divide by the standard deviation... so what if you don't do these operations?
Mar
19
comment What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
I've added some Python code that verifies this with eigenvectors and Monte Carlo, and added a bit of discussion. Hopefully it clears things up now.
Mar
19
revised What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
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Mar
19
revised What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
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Mar
19
revised What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
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