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14h
comment Prove that $\frac{x}{y}+\frac{y}{z}+\frac{z}{x} \geq 3$ for $x,y,z>0$
Try AMGM inequality
1d
comment $L_{\infty}$ norm
Try Swapping the integral and summation. Does that help you see it?
Jun
28
accepted A Taylor series expansion of $e^{ix}$
Jun
28
comment A Taylor series expansion of $e^{ix}$
Oh, so there was an error in the book. Didn't realize it. Thanks. Good use of induction.
Jun
28
revised A Taylor series expansion of $e^{ix}$
added 249 characters in body
Jun
28
comment A Taylor series expansion of $e^{ix}$
No. What I am asking is if anyone knows how to derive (2). And note that I mentioned "Taylor Theorem" i.e. I am looking for something like this: $f(z) = f(0) + zf'(0) +... + \frac{z^n}{n!}f^{(n)}(s)$ for some $s \in \mathbb{C}$. I'm not sure how to write it for complex valued functions or if it is true at all.
Jun
28
asked A Taylor series expansion of $e^{ix}$
Jun
27
comment Is there only one set of KKT conditions for a given optimization problem?
How is it the same optimization problem if you remove the equality constraints?
Jun
26
answered Probability of Limsup of a bunch of events
Jun
26
revised Probability of Limsup of a bunch of events
added 25 characters in body
Jun
25
revised Probability of Limsup of a bunch of events
added 355 characters in body
Jun
25
reviewed Approve What is the significance of squaring a number?
Jun
25
asked Probability of Limsup of a bunch of events
Jun
24
comment Ratio limit of moments for bounded functions
Yes. The proof is correct. Although I would advise for the sake of rigour to use limsup and liminf wherever applicable since the limits of the quantities in question are not known to exist beforehand.
Jun
15
revised How can we simplify the expression $P+\sqrt{ (P^2+\sqrt{ (P^4+\sqrt{ (P^8+…)}}}$?
Formatting
Jun
15
comment How to apply strong law of large numbers for non-constant mean and variance
You might find this useful: math.stackexchange.com/q/418537/35983. Also start with $P[|\frac{\sum_{k=1}^nX_k}{n} -1| > \epsilon]$ and use Chebyshev's Inequality. Let us know what happens. As for LLN, it cannot be directly applied as the variables are not identically distributed but that doesn't mean the result can't be proved...
Jun
15
comment Riesz representation theorem
Yes. Since a linear functional is after all scalar valued and nonzero here. Tackle the zero case separately.
Jun
15
answered Riesz representation theorem
Jun
15
comment prove : if E(X) doesn't exist $E(x^2)$ too doesn't exist.
@Arnob: It is indeed due to Cauchy Schwarz. And as for your inequality, if you were to integrate restricted to $\{x:|x| \geq 1\}$, it would be fine.
Jun
15
comment prove : if E(X) doesn't exist $E(x^2)$ too doesn't exist.
Square the LHS and you will be fine.