5,085 reputation
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bio website quantdec.com
location Northeastern US
age 14
visits member for 4 years, 4 months
seen 2 days ago

Consultant (environmental and spatial stats a specialty), expert witness, and teacher. I can be reached through (outdated but still valid) links posted on my web site.

Twitter: @WilliamAHuber // ASA-P website: http://amstatphilly.org/


Why waste time learning, when ignorance is instantaneous?

--T(iger) Hobbes.

For any complex problem there is a simple solution. And it's always wrong.

--[Mis?]attributed to H.L. Mencken by Dava Sobel, Longitude.


Aug
31
comment Finding the Heavy Coin by weighing twice
Thank you, Yaser. I hope people notice that your explanation not only is detailed and complete but also is the shortest one so far.
Aug
31
comment Finding the Heavy Coin by weighing twice
@Moron: Yaser Sulaiman's explanation looks clear and helpful to me.
Aug
31
comment Finding the Heavy Coin by weighing twice
What's the down vote for? This answer is a strong hint intended not to spoil an easy puzzle. (If you remove 95 coins you've reduced the problem to finding one heavy coin out of five coins containing at least one heavy one.)
Aug
31
comment Finding the Heavy Coin by weighing twice
@Chandru1: I will after you pay me.
Aug
31
answered Mental card game
Aug
31
comment Is there a name (and use) for an average based on the unique values of a set of data?
One amusing possibility is that the dataset represents a random sample (with replacement) from an urn known to contain finitely many distinct values. An average like the one proposed here is likely to be a better estimator of the population average than the usual average. (It's definitely a better estimator in some cases where the number of distinct values in the population is known.)
Aug
31
answered Finding the Heavy Coin by weighing twice
Aug
31
answered Integrate product of Dirac delta and discontinuous function?
Aug
31
answered Is there a name (and use) for an average based on the unique values of a set of data?
Aug
31
comment Units of $M_2(Z)$
Sure your second part talks about determinants, Arturo: it's entirely about the expression D = ad - bc, which clearly is integral whenever a, b, c, d all are. A simple calculation establishes that the corresponding expression for the inverse (as explicitly given in the question) equals D/D^2 = 1/D, whence D must be a unit, QED.
Aug
30
comment Units of $M_2(Z)$
Your argument could be shortened by referring to the coefficients of the inverse matrix provided in the question itself: computing their determinant shows the determinant of the inverse matrix equals 1/(ad-bc) and we're done, because determinants of integral matrices are obviously integral.
Aug
30
answered Units of $M_2(Z)$
Aug
30
answered Nth derivative of a function: I don't know where to start
Aug
30
comment A naive approach for nonlinear optimization on several real variables and one natural variable. Give examples of (potential) failure
@Mariano: I see. Thanks.
Aug
30
comment How to prove Euler's formula: $e^{it}=\cos t +i\sin t$?
There appear to be some gaps here; the most significant one concerns the use of a complex logarithm. You seem to have overlooked the fact there are many more solutions to exp(C) = 1 than merely C = 0. Their existence is an implication of Euler's formula itself. To avoid circular logic, the crucial thing is to make clear what definitions you are using for exp, sin, and cos (and also, in this case, of the complex logarithm).
Aug
30
comment A naive approach for nonlinear optimization on several real variables and one natural variable. Give examples of (potential) failure
@Mariano Suárez-Alvarez: true, 1 = 1 is technically an "equality constraint," but the mathematical interest in constraints is due in part to the fact that a collection of constraints can confine the feasible region to a compact space and in part to the existence of boundaries and even corners in that space (it is a manifold-with-corners); those corners can play an important role in optimization algorithms.
Aug
29
comment A naive approach for nonlinear optimization on several real variables and one natural variable. Give examples of (potential) failure
It appears that this is an integral program, not a real program. The optimum of a function of a set of integers is being found by obtaining it over a real extension and then rounding to nearby integral coordinates. The question concerns why this might be a bad approach.
Aug
29
answered A naive approach for nonlinear optimization on several real variables and one natural variable. Give examples of (potential) failure
Aug
29
comment Intuition for the definition of the Gamma function?
@Qiaochu: The final paragraph was put there precisely to avoid being accused of using a trick! ;-) The reference to statistics is that the study of variances leads one to look at the distributions of sums of squares of Gaussian variables (called chi-squared distributions). Obtaining volumes of hyperspheres drops out almost by accident as a byproduct of this calculation.
Aug
29
comment Intuition for the definition of the Gamma function?
@Qiaochu: The method of stationary phase (Tao's notes), btw, is motivated by the central limit theorem. The gamma distribution, as you now know from other comments and another answer, is a sum of independent exponentials. The CLT implies it should be close to Gaussian for large n. This means the integrand should be well approximated by a parabolic fit to its logarithm. A good choice is the Taylor series around the maximum. This lets us approximate the integral by the Normal integral (equivalently, erf) with parameters depending on n, whence we obtain asymptotic formulae.