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 Aug30 comment Is $\exp(-2\sin^2t)$ a characteristic function? @snarski i assume the former. but if you know the latter, even better?/ Aug26 comment How do I prove convergence of the recursive sequence $c_n = c_{n-1} + \frac{0.01}{n}$? This diverges because ^ Aug15 comment Has anyone ever won a field medal for inventing stochastic calculus? Your answer now needs an update because of Martin Hairer. :) Aug8 comment Angle between $(X,Y)$ and $(E(X), E(Y))$ where X and Y are independent random variables. @Alex how do you define angle with, say 3, variables? Aug4 comment If $a_1a_2\cdots a_n=1$, then the sum $\sum_k a_k\prod_{j\le k} (1+a_j)^{-1}$ is bounded below by $1-2^{-n}$ Please consider accepting an answer by pressing the tick when you are happy. I realized you have not yet accepted any answer. Jul24 comment Upper bounding a Poisson Process with indicators of exponentials $\mathcal{E}\sim\exp(\lambda)$? <- doesn't meant $N$ no longer takes integer values.? Jul24 comment Ergodic properties of orthogonal group $O(n)$ Please consider accepting some answers for the 104 questions you asked. Jul24 comment Evaluating $\int^b_a \frac{dx}{x}$ from the definition of the integral What I do not understand is, what is a Harmonic number when $bn/(b-a)$? Jul24 comment Why left multiplication when it comes to Markov chains? Because $P_{12}$ is prob from state 1 to 2, not vice versa Jul23 comment Expected number of changes of serves in a game of raquetball @ian i was lazy but should have spotted the 0.1428 to be honest... Jul23 comment Expected number of changes of serves in a game of raquetball @orio1909 because the Markov Chain is aperiodic and recurrent, so it will always converge to its stationary distribution. Jul22 comment What did I do wrong when using Jacobian transformation Can you please write out how you did the transformation? This is bog standard. Jul22 comment Trace of power of stochastic matrix @pisoir so what are you trying to show? Jul22 comment Trace of power of stochastic matrix you are essentially asking how does the overall probability that a state remains where it is in 1 move compare with a state remains where it is in 2 moves... Jul22 comment Trace of power of stochastic matrix nevertheless, it is still false, change the $0$ to a small $\epsilon$. Jul22 comment Asymptotics of sum of binomial distributions +1, thanks again. Jul22 comment Expectation related to Normal distribution and its density I seem to get this to be true only when $\sigma< 1$... and that might sense somewhat. Jul22 comment Expectation related to Normal distribution and its density You were probably too wasteful throwing away the $\Phi$ term. Jul21 comment The mathematical odds of winning a hand in poker with two boards Nevertheless I actually don't think ^ matters much. The losing player has a better chance of keeping the money (so does the winning player). Jul21 comment The mathematical odds of winning a hand in poker with two boards This would surely also depend on many more things: on how many overcards does the player with a flush draw have? whether the player with the pair is holding one of the outs for the flush? Was the pair a pocket pair? etc. You should give a specific combination of cards, then I am happy to calculate these for you.