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 Apr20 comment Why the two expressions of total variation distance are equivalent? When positive difference and negative difference appear together, they compensate each other. So the maximum is achieved with either as many as possible positive differences or as many as possible negative differences. Since we are dealing with probability measures, the absolute values of all the positive differences and of all the negative differences are the same Apr16 comment Expectation Proof Apply Jensen's inequality with $f(x)= x\ln x$ Apr16 answered Adaptive gambler's ruin problem Apr16 answered Proving that $\lim_{n\rightarrow\infty}n(a_{n+1}-a_{n})=1 \implies a_n$ diverges to $\infty$ Apr9 reviewed Reviewed Writing the possible values of “x” in an equation or making a solution check at the end? Apr9 revised Writing the possible values of “x” in an equation or making a solution check at the end? added 7 characters in body Apr9 reviewed Close Someone please help tried everything Apr9 reviewed Approve How can we use an identity to solve the equation $1-\tan^2 \theta = \frac{2}{3}$? Apr8 answered How can I prove this property of binomial coefficients? Apr8 revised Rule of 72 doubling time added 9 characters in body Apr8 answered Rule of 72 doubling time Apr8 comment A theorem on the standard uniform distribution $F_\xi(x)$ is a determinisitic function, and you apply it on the random value of $\xi$ to get another random value $F_\xi(\xi)$ Apr6 comment What is the motivation of Levy-Prokhorov metric? One can write $L(F,G)$ slightly differently as $$L(F,G) = \inf\{\epsilon > 0| F(x) \leq G(x+\epsilon) + \epsilon \text{ and } G(x) \leq F(x+\epsilon) + \epsilon, \forall x\in \mathbb{R}\}$$ so that more clearly L-P metric is a generalization of Lévy's metric Mar20 comment How to prove this Brownian motion convergence? If $X \to Y$ almost surely and $E(X^2) \to 0$, we have $Y=0$ by Fatou's lemma Mar8 reviewed Leave Open Can such function exist? Mar8 reviewed Leave Open Is there a definite integral that evaluates to the constant $e$? Mar8 answered Derivative of a piecewise function with x=0 Mar8 comment Sequence of rational number converging to a irrational number $\beta$. @S.C. nothing is special with $10$, other examples that you mentioned work as well Mar8 comment Sequence of rationals converges to an irrational for (a), see this Mar8 answered Convergence of ratio of linear combination of iid random variables to their sum