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Apr
20
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
Apr
16
comment Expectation Proof
Apply Jensen's inequality with $f(x)= x\ln x$
Apr
16
answered Adaptive gambler's ruin problem
Apr
16
answered Proving that $\lim_{n\rightarrow\infty}n(a_{n+1}-a_{n})=1 \implies a_n$ diverges to $\infty$
Apr
9
reviewed Reviewed Writing the possible values of “x” in an equation or making a solution check at the end?
Apr
9
revised Writing the possible values of “x” in an equation or making a solution check at the end?
added 7 characters in body
Apr
9
reviewed Close Someone please help tried everything
Apr
9
reviewed Approve How can we use an identity to solve the equation $1-\tan^2 \theta = \frac{2}{3}$?
Apr
8
answered How can I prove this property of binomial coefficients?
Apr
8
revised Rule of 72 doubling time
added 9 characters in body
Apr
8
answered Rule of 72 doubling time
Apr
8
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 $F_\xi(\xi)$
Apr
6
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
Mar
20
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
Mar
8
reviewed Leave Open Can such function exist?
Mar
8
reviewed Leave Open Is there a definite integral that evaluates to the constant $e$?
Mar
8
answered Derivative of a piecewise function with x=0
Mar
8
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
Mar
8
comment Sequence of rationals converges to an irrational
for (a), see this
Mar
8
answered Convergence of ratio of linear combination of iid random variables to their sum