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 inequality
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Aug
7
awarded  inequality
Aug
6
comment If $ab(a+b)=2$ then what will be the value of $\frac{1}{(ab)^3}-a^3-b^3$?
take $a=1, b = -2$, then the conclusion is not ture
Aug
6
answered Two inequalities for $\left(\int_{a}^{b}|f(x)|^rdx\right)^{\frac{1}{r}}$
Jul
14
answered $a_1,a_2,…,a_n$ are positive real numbers, their product is equal to $1$, show: $\sum_{i=1}^n a_i^{\frac 1 i} \geq \frac{n+1}2$
Jul
12
comment Compute almost sure limit of martingale?
@BCLC $Y$ and all the $Y_m$'s are i.i.d. i.e. independent and identically distributed
Jul
12
comment Compute almost sure limit of martingale?
@BCLC $P(Y=1) < 1$ excludes the case where $Y$ is a constant almost surely, so Jensen's inequality is strict
Jul
12
comment Compute almost sure limit of martingale?
@BCLC An independent copy of $Y_1$
Jul
9
awarded  Nice Answer
May
27
comment Total variation distance is complete
@DavideGiraudo Thank you! so the conclusion is that the total variation distance is complete for general $X$
May
27
accepted Total variation distance is complete
May
26
asked Total variation distance is complete
May
1
answered Evaluating $\sum_{n=1}^\infty \frac{n^2}{3^n} $
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 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?