1,700 reputation
516
bio website mathtm.blogspot.com
location University of California Los Angeles, CA
age
visits member for 2 years, 8 months
seen 10 hours ago

I am a recent graduate in applied mathematics at UCLA and currently trying to break into the quantitative investment/trading industry while also continuing to pursue advanced graduate-level mathematics as both a hobby and career necessity.


May
6
revised Find $[E(Y^2)]$. When $Y = 3 * X - 5$ and $X$ is distributed in range $[0, 5]$
edited body
May
6
answered Find $[E(Y^2)]$. When $Y = 3 * X - 5$ and $X$ is distributed in range $[0, 5]$
May
6
answered Fourier transform and sufficient condition…
May
6
answered Consider the differential equation: $y'=\frac{x^2}{1-y^2}$
Apr
29
comment Left sided limit of an Riemann-Stieltjes integral
Yes, that's fine, since $\alpha$ is left continuous at $b$ and $|f|$ is bounded by the assumption $f\in\mathscr{R}(\alpha)$.
Apr
28
comment What is $\int e^{-\frac{(y-\mathbf{x}^T\mathbf{\theta})^2}{2}}d\mathbf{\theta}$?
It's the same thing. You're just taking one more step.
Apr
28
comment Need to find infimum S!!
^ essentially, yes. And using your calculator to plug in sample values is not an acceptable argument. It is sometimes helpful for giving you intuition and an idea of what the answer should be, but in this situation you need to apply some additional reasoning.
Apr
28
answered Need to find infimum S!!
Apr
28
comment Need to find infimum S!!
How exactly are you coming up with the number -0.98? It's quite obvious that it can't be this, since there is an $n$ such that $-1\leq\cos(\pi\sqrt{n}/2)<-0.98.$ The periodicity of $\cos$ then allows you to take $n$ large enough so that $2/n$ is as small as you like.
Apr
28
answered What is $\int e^{-\frac{(y-\mathbf{x}^T\mathbf{\theta})^2}{2}}d\mathbf{\theta}$?
Apr
28
comment Left sided limit of an Riemann-Stieltjes integral
Of course, but $\sum m_{i}\Delta\alpha_{i}\neq(\alpha(b))-\alpha(c))\sum m_{i}$ unless $m_{i}$ is also independent of $i$ on all partitions (i.e. $f$ is constant). And in any case, it still doesn't give you the right to pull $\Delta\alpha_{i}$ out of the sum since $\Delta\alpha_{i}\neq\Delta\alpha_{j}$ for $i\neq j$ in general unless $\alpha(x)=x$, or $\alpha(x)=\text{constant}$ (in which case the integral is $0$ no matter what $f$ is).
Apr
26
comment Left sided limit of an Riemann-Stieltjes integral
Unless $\alpha$ is uniform, i.e. Lebesgue measure, you can't take it out of the sum like that since it depends on the partition interval (even if your partition is evenly spaced). In other words, in no circumstance is $\Delta\alpha_{i}=\Delta\alpha$ (whatever the right hand side is) except where $d\alpha=dx.$ Moreover, $\Delta\alpha\neq\alpha(b)-\alpha(c)$ in this situation. You need to work on your solution, but the general idea is correct.
Apr
26
answered Why it is bounded?
Apr
25
revised Question about Volume of a cube
added 2 characters in body
Apr
25
revised Question about Volume of a cube
added 341 characters in body
Apr
25
answered Question about Volume of a cube
Apr
25
answered Left sided limit of an Riemann-Stieltjes integral
Apr
25
answered Definite Integral of $1+\sqrt{9-x^2}$?
Apr
18
comment Integral of $\sin^{-1}(1/2 - \sin x) dx$
A quick check on Wolfram reveals that the answer is likely no (by solution, I assume you mean a closed formula for the indefinite integral).
Apr
17
answered Let $M$ be a bounded subset of the space $C_{[a,b]}$. Prove that the set of all functions $F(x)=\int^{x}_{a}f(t)dt$ with $f\in{M}$ compact.