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 Dec28 comment How to show that show that $\frac{v+u}{1+ uv/c^2}=c$ when $u=c$? I'm guessing that you really mean $(u+v)/(1 + \frac{uv}{c^2})$, not $u+\left(v/(1 + \frac{uv}{c^2})\right)$. Dec19 comment Finding the points of intersection of a circle and a line In Exercise 2, your two points do not satisfy $x + y - 1 = 0$. Dec5 comment What is a simple example of an unprovable statement? Do you have a reference to this problem or ErdÅ‘s's paper? 5 minutes of Googling didn't turn it up, but that may be because your (nice) presentation of it isn't the canonical one. Oct5 comment Expected deviation of a coin that obeys the gambler's fallacy My attempt to prove via induction that the variance is $\frac n {12}$ continues but is kind of in the weeds. Having that closed form of the probability of $h$ heads after $n$ flips couldn't hurt. The recurrence given on the Wikipedia page bears enough resemblance to the formula for $H(n)$ that I assume a proof that the probabilities are actually Eulerian is straightforward. Sep30 comment Expected deviation of a coin that obeys the gambler's fallacy Calculation "by hand" (with a Python program) indicates that for $n \ge 3$, the variance is $\frac{n}{12}$ so the standard deviation is $\frac{1}{2\sqrt3}\sqrt n$. If I'm able to prove it (induction seems promising), I'll add the proof as an answer. Aug27 comment A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white. If the book calls it "Baye's Theorem", I would not trust the book. Jun4 comment 'Obvious' theorems that are actually false You order the rationals $q_1, q_2, \ldots, q_n, \ldots$ and place an interval of $(\frac \epsilon 2)^n$ around each one, choosing $\epsilon$ to be less than $1$. May23 comment Are mathematical articles on Wikipedia reliable? I was curious whether Nature had a response to the response, and they did, here and here. (I have no contribution to make regarding which side is in the right; I'm just presenting the documents for others who are curious). May1 comment Examples of mathematical results discovered “late” It took a surprisingly long time (17th century) for even very basic concepts of probability theory to be developed, considering that those concepts would have been immensely valuable in real life, given that gambling has been popular forever. Apr17 comment Is there any shorthand notation for linear interpolation? pic also accepts a of the way between p and q, which I suppose demonstrates the lack of a common notation. Apr17 comment Is there any shorthand notation for linear interpolation? @MJD Thanks. After a little searching, it looks like the pic notation is a and metafont's is a[p,q], so they do have the same general form. Apr4 comment how to calculate this convolution: That function looks a little funny. Is it possible that $u(t) - (t-T)$ is really $u(t) - u(t-T)$ and you copied it down incorrectly? I'm also a little surprised that the problem bothers to give two names $x(t)$ and $h(t)$ to the same function. Apr3 comment Solving $y'-y=2\cos 5t$ using the Laplace Transform Note by the way that you can do the partial fractions part of this problem (which is most of it!) a lot easier by using the cover-up method. The time spent learning this method will have paid for itself by the time you've done two Laplace transform problems. Apr3 comment Solving $y'-y=2\cos 5t$ using the Laplace Transform You can easily check your answer for $y(t)$ by just seeing whether the original differential equation holds for it. Apr1 comment Confusing rational numbers I haven't checked your intermediate math, but perhaps you are expected to rationalize the denominator in your final answer? Mar30 comment Strategies for developing explicit formulas for nth term given recurrence relation? The closest thing to a general method for solving recurrences is the use of generating functions, which will definitely work in this case. Searching for "generating functions recurrence" will turn up some material. If you want a textbook reference, try Concrete Mathematics by Graham, Knuth, and Patashnik, or An Introduction to the Analysis of Algorithms by Sedgewick and Flajolet. Mar28 comment Probability of getting no worms in your box One quick check for whether your formula for exactly $n$ infested boxes is correct is that if you sum the probabilities for $n=0$ through $n=6$, you should get $1$, since that covers all the cases. Mar28 comment Probability of getting no worms in your box The probability that exactly $n$ out of the $6$ boxes are infested is a more complicated problem, and you would have to use the formula for a binomial distribution. Mar23 comment Roulette with extraordinary strategy Do you have any knowledge of probability theory already or are you solving this totally from first principles? Mar22 comment Limit question involving L'Hospitals rule I agree with you!