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Quantitative analyst and math blogger.


Feb
18
revised What is my interest rate?
Added new answer
Feb
18
answered What is my interest rate?
Feb
4
comment Expected value of first head in coin toss.
Since $X$ is a discrete random variable, you should take the sum $\sum_x x f_X(x)$, not the integral.
Feb
2
awarded  Nice Answer
Jan
31
comment Inverse birthday estimation
Possible duplicate of math.stackexchange.com/questions/114544/… ?
Jan
31
comment Inverse birthday estimation
Yes, it's natural log. I don't know a name for this problem, although that doesn't mean there isn't one.
Jan
31
answered Inverse birthday estimation
Dec
31
comment What's the name of this quantity?
We have $M_n \ge \lfloor n^2/2 \rfloor$, since $dist(\sigma_n) = \lfloor n^2/2 \rfloor$ when $\sigma_n$ is the ``reverse'' permutation $n(n-1)(n-2) \ldots 1$. This is the sequence oeis.org/A007590. But I can't prove that this is an equality.
Dec
12
comment Proof of inequality with ratio of odds to evens.
This actually may have to do with calculus, depending on what you've learned - take logs of all three members of the inequality and you've converted the problem into showing that a certain sum is between $-\log 2 - \log n$ and $-{1 \over 2} \log 2 - \log n$. If my intuition is right, there are two integrals which are lower and upper bounds for that sum and which have those values. (Comment instead of answer because I haven't worked out the details so I don't know if this works.)
Oct
28
comment Maximum bin load for $\alpha n$ balls into $n$ bins
It would help if you gave a reference to the paper.
Oct
26
awarded  Nice Answer
Oct
24
awarded  Generalist
Oct
4
comment Baseball, batting average, and probability
Sabermetrics folks have already looked into this: see for example here, here, here.
Sep
8
awarded  Good Answer
Aug
31
answered Probability that centre of the square lies inside the circle joining the two points inside the square
Aug
26
awarded  Nice Question
Aug
22
comment Elementary statistics problem
If you're being asked to solve this problem, you have probably seen a few inequalities named after Russians.
Aug
19
comment Longest known sequence of identical consecutive Collatz sequence lengths?
That's because the "Collatz path" of nearby numbers often coalesces. To take a simple example, there are sequences starting 36-18-9-28 and 37-112-56-28. Both have one upward step and two downward steps, but in different orders. Lopsy's heuristic doesn't know about this.
Aug
19
comment Longest known sequence of identical consecutive Collatz sequence lengths?
See oeis.org/A008908. There's a sequence of length 17 starting at 7083. After 36 steps, the sequence of iterates of 7083 through 7099 all coalesce at 76; they all reach 1 at step 58.
Aug
18
comment Longest known sequence of identical consecutive Collatz sequence lengths?
I'd note that this depends on how you define "Collatz sequence" - does an odd n get mapped to 3n+1, or to (3n+1)/2? (You've chosen the first one.)