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 Yearling
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May
3
reviewed Approve Show that there exist $k$ and $r$ such that the given sum is divisible by $n$
Apr
23
awarded  Yearling
Apr
20
reviewed Approve Proof of Equivalence of Sets
Apr
19
reviewed Approve Prove that for all positive integers $n$, $2^1+2^2+2^3+…+2^n=2^{n+1}-2$
Apr
18
reviewed Approve $X_1, \dots, X_n$ are independent random variables. Suppose $M = \min(X_1, X_2, \dots, X_n)$
Apr
18
reviewed Approve coordinate geometry : intersection of a curve with a line
Apr
7
comment Prove that if $0\leq a,b$ and $a+b=1$ then $x^ay^b\leq ax+by$ for $x, y >0$
This is known as Weighted AM-GM Inequality. Check out proofs here and here.
Mar
24
comment Why is the conditional probability treated as a definition in Kolmogorov's probability theory?
Interesting. So, you are basically asking why should we not define conditional probability as the most basic form of probability, so that the current definition of conditional probability comes out as a some lemma or theorem. This will probably require some notion of conditional measures. Most likely what might happen is we will end up pushing the current conditional probability definition and generalize it to general measures (if that is possible). So, we won't be able to get rid of the intuitive definition. Also, I can't see any particular advantage of a general conditional measure.
Mar
23
answered Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
Mar
23
answered Simple integral calculation: $\int \sqrt{x^2-4}\,dx$
Mar
20
reviewed Approve Sum of a power series $n x^n$
Mar
20
reviewed Approve analysis problem of continity
Mar
20
comment $T$ is a linear operator
You seem to have the right idea, but your notation is messed up. From what is given to you, $(Tx)_i = \frac{x_i}{i}$, use it to write your earlier post clearly.
Mar
20
comment $T$ is a linear operator
Look at $(Tx)_i$, $(Ty)_i$ and $(T(x+y))_i$, what can you conclude? Look at $(T(kx))_i$ and $k(Tx)_i$, what can you conclude? What does the above tell you about T? For the norm part, what is norm $\|Tx\|$ (remember $Tx \in l^2$)? Does it remind you of some well known inequality?
Mar
20
revised $T$ is a linear operator
Latex Corrections
Mar
19
awarded  Citizen Patrol
Mar
18
comment How to use CVX to solve this problem?
CVX can accept the form as it is, although I am not quite convinced that your objective function is convex.
Mar
18
comment Prove Trigonometric Identitiy
@ArpanBanerjee You are correct.
Mar
18
comment Prove Trigonometric Identitiy
Indeed, you are correct.
Mar
18
comment Prove Trigonometric Identitiy
It is not a good idea to multiply and divide by a term that can be zero for certain values. In your case, your term is zero for a = 0.