|
Jul
13 |
|
revised |
Closed formula for probability of n-digit numbers containing three consecutive sixes approximation |
|
Jul
13 |
|
comment |
'deducing' a bound using the first order taylor series. How to make it more precise? Wikipedia suggests $\sqrt{2 \log_e(2)}\sqrt{n} + 0.26895 \lt r \lt \sqrt{2 \log_e(2)}\sqrt{n} + 1.27921$, which for most $n$ will give a single integer in that interval. |
|
Jul
13 |
|
revised |
Closed formula for probability of n-digit numbers containing three consecutive sixes dupe |
|
Jul
13 |
|
comment |
Existence of Borel set and probability measure $\omega$ is an unfortunate choice of notation for the probability measure, when it is typically used to indicate an element of $\Omega$. |
|
Jul
13 |
|
comment |
Methods for Finding Raw Moments of the Normal Distribution @student1 - I think it is well known: a quick search turns up for example davegiles.blogspot.com/2019/04/… |
|
Jul
12 |
|
answered | Closed formula for probability of n-digit numbers containing three consecutive sixes |
|
Jul
12 |
|
comment |
How does anyone know for sure who the Prime Minister is? In 1945, it was not clear that Attlee would remain leader of the Labour Party - he had been elected in 1935, but most of the 1945 Labour MPs were new. He went to the palace anyway, and (from Wikipedia) the notoriously laconic Attlee and the famously tongue-tied King stood in silence; Attlee finally volunteered the remark, "I've won the election". The King replied "I know. I heard it on the Six O'Clock News". |
|
Jul
12 |
|
comment |
How does anyone know for sure who the Prime Minister is? It is worth noting that the new Westminster parliament had not met on 5th July 2024 and would not meet until 9th July to elect a Speaker: in fact when Keir Starmer went to see the King in the morning of 5th July, several constituencies had not counted their votes and did not know who their MP would be. But enough had and the result was obvious and Rishi Sunak had resigned, advising the King to send for Keir Starmer, so that is what happened. |
|
Jul
12 |
|
comment |
Voter Count(similar to Bertrands ballot theorem) Why is it "without crossing the line $y=\frac{m}{n+m}x$" rather than "without crossing the line $y=x$"? |
|
Jul
12 |
|
comment |
Optimal number of answers for a test with wrong-answer penalty A curiosity is that without the "ten question" limit but still with the $5$ point pass mark, the optimal number of questions to answer would be $32$. |
|
Jul
11 |
|
answered | Making a mixture of Gaussians unidentifiable? |
|
Jul
11 |
|
comment |
Making a mixture of Gaussians unidentifiable? Or perhaps $\text{sign}(X)$ |
|
Jul
11 |
|
comment |
Making a mixture of Gaussians unidentifiable? Perhaps try something like $\frac{X}{A}$. |
|
Jul
11 |
|
comment |
Closed form for the partial sums of the Harmonic Series? If the denominator is $n!$ then the numerator is OEIS A000254 |
|
Jul
11 |
|
comment |
How to quantify the "degree of convergence" so some number? Take an example of $f(n)=\sum\limits_{k=0}^\infty (-1)^k\left(1-\frac1n\right)^{2^k}$. The initial terms (rounded) $0, 0.309, 0.382, 0.414, 0.429, 0.440, 0.449, 0.456, 0.463, 0.468, \ldots$ etc. look as if they may be converging towards something close to $0.5$, but it does not converge. |
|
Jul
11 |
|
comment |
Which distributions have nice closed form expressions for expected value of exponential? For $\mathbb E\left[e^{-kX}\right]$ this is essentially the moment generating function with a sign change |
|
Jul
10 |
|
comment |
Definition of elementary conditional expectation through measure-theoretic conditional expectation I am not sure what $\mathbb{P}(Y\in B\mid X)(\omega)$ and $\mathbb{E}(Y \mid X)(\omega)$ mean here. |
|
Jul
10 |
|
comment |
Why is it possible to generate a random real from the uniform distribution, but not a random rational from an equivalent distribution?? There is no uniform distribution on a countably infinite set since for mutually exclusive events you have $P\left(\bigcup\limits_{i = 1}^\infty E_i\right) = \sum\limits_{i=1}^\infty P(E_i)$: if all the $P(E_i)$ were equal, you would either get a total probability of $0$ or get $\infty$ when it should be $1$. |
|
Jul
10 |
|
revised |
Why doesn't the linear regression preserve the standard deviation? colours |
|
Jul
9 |
|
comment |
Boolean NOT is missing: the count of items in set A but not in set B is the count of items in either set less the count of items in B, right? @CyclotomicField I suspect the "-" in "(A OR B) - B" may be intended to be arithmetic subtraction, while "A NOT B" may be set difference |