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Consultant (environmental stats a specialty) and teacher.


Jan
5
answered Optimisation problem; Length of a cable
Jan
5
comment A question about symmetric bilinear forms
The examples of the zero matrix (indefinite but degenerate), the identity matrix (nondegenerate and positive definite) and the diagonal matrix $(1,-1)$ (nondegenerate and indefinite) resolve both questions in the negative.
Jan
4
awarded  Nice Answer
Jan
4
revised What's a proof that the angles of a triangle add up to 180°?
edited body
Jan
4
comment What's a proof that the angles of a triangle add up to 180°?
@Joe You are right: I meant $1,i,-i,-1$, in that order (although your construction works just as well). I'll fix it--and thanks for reading so carefully!
Jan
4
comment What's a proof that the angles of a triangle add up to 180°?
It is interesting that the conclusion follows from Assumption (1). However, this requires proof. After all, it is not true in other closely related geometries (such as spherical or hyperbolic geometries).
Jan
4
answered What's a proof that the angles of a triangle add up to 180°?
Jan
4
comment What's a proof that the angles of a triangle add up to 180°?
@Meysam Geogebra is a free Java application designed for geometric illustrations. It's mature and works well.
Jan
4
comment How to solve this algorithmic puzzle?
Thinking about this problem recursively looks fruitful: in many cases, making $[a_1, \cdots, a_{n-1}]$ normal will automatically normalize $[a_1, \cdots, a_n]$. Consider, then, how to characterize the lists for which you must operate on $a_n$ in order to normalize them optimally. If your list is one of them, operate on $a_n$. In any event, proceed to recursively solve the problem for $[a_1, \cdots, a_{n-1}]$. The complication to deal with is when $a_n$ is a maximum and the final $T$ elements of the list are not normal.
Jan
3
comment Invariant inner products on infite-dimensional representations
$G$-invariant objects are often constructed by averaging over the group. You can average over a compact group by using its invariant measure (which is finite because the group is compact: the averaging becomes problematic when the measure of the group is infinite), so many statements about representations of finite groups carry over to compact groups, mutatis mutandis, with almost no additional effort.
Jan
3
comment What's a proof that the angles of a triangle add up to 180°?
I see that rschwieb recently sketched the same approach. The figure may help in understanding it and the appeal to properties of the affine group should help make it rigorous, especially insofar as a crucial gap--proving the coincidence of $A_1'$ and $C'$--is concerned.
Jan
3
answered What's a proof that the angles of a triangle add up to 180°?
Dec
31
comment Finding the analytic function
One approach exploits the answers to the closely related question at math.stackexchange.com/questions/267514: consider the real part of the inverse of $f'$.
Dec
27
comment Regressing $Y$ back on the residuals
Hint: When you think of $y$, $x$ and $\hat{e}$ as vectors, the normal equations assert that $\hat{e}$ is orthogonal to $x$. When (after centering $x$ and $y$) you write $y = 1 \cdot \hat{e} + b x$, the residuals--thinking of $\hat{e}$ as the variables this time--are $b x$. If you could somehow show $b x$ is orthogonal to $\hat{e}$, this would demonstrate that you have indeed regressed $y$ against $\hat{e}$.
Dec
27
comment Distribution of the number of children needed so that at least both a girl and a boy are born
Right, but your formula gives a "probability" of $-1$ in the case $k=0$, whereas it should be $0$.
Dec
27
comment Distribution of the number of children needed so that at least both a girl and a boy are born
(1) Take care when $k=0$. (2) What question are you answering? The current one asks for a "distribution" of $N$. (I believe this question needs further clarification in order for the meaning of this request to be properly understood.)
Dec
27
comment Absolute continuity inquality
You may have neglected some additional assumptions: after all, for $u(x)=1$ the rhs is zero while the lhs diverges toward $+\infty$.
Dec
26
comment Why is $\log(\sqrt{x^2+1}+x)$ odd?
It is also crucial that the integral start at $0$ and not someplace else.
Dec
6
comment How to show that the inverse Gaussian density integrates to 1?
One method: look up the CDF (in Wikipedia, say) and differentiate it to prove it is correct. Then evaluate its rightmost limit. Both processes are purely mechanical.
Dec
6
comment How to show that the inverse Gaussian density integrates to 1?
These links seem to address a substantially different question of integrating a Gaussian density rather than the inverse Gaussian.