180 reputation
7
bio website
location Santa Cruz, CA
age 28
visits member for 2 years
seen 2 days ago

Ph.D. Student of Computer Engineering at University of California, Santa Cruz.

M.Sc. in Computer Science from University of Calgary.

B.Sc. in Computer Engineering from Sharif University of Technology.


Mar
10
awarded  Popular Question
Mar
7
asked Finding a base for a series to sum to a constant
Nov
18
comment Markov chains: simple random walk $S_n$
Suppose that you are at origin and start moving away at discrete random increments. What I understand from your statement is that the probability of being at distance $i$ from the origin at the $n$-th stage of your walk given that you have been at distance $i-1$ in the $n-1$-th stage is given as $\frac{p^i}{p^i+q^i}$.
Nov
18
awarded  Teacher
Nov
18
answered Markov chains: simple random walk $S_n$
Nov
18
awarded  Commentator
Nov
18
comment Calculating expectation of a random variable knowing expectation of a function of it
@StephenMontgomery-Smith: Fair enough. Then, I better rephrase my question as what other information about $X$, except its density function, help attain a tighter bound for (or the exact value of) $\mathbb{E}[X]$?
Nov
18
comment Calculating expectation of a random variable knowing expectation of a function of it
@StephenMontgomery-Smith: Ah, I see. But $X$ is not necessarily a constant random variable.
Nov
18
comment Calculating expectation of a random variable knowing expectation of a function of it
@DilipSarwate: I just know $\mathbb{E}[a^X]$ for a specific positive constant $a$ and not as a function of $a$. I am kind of familiar with the concept of moment-generating function, but cannot see how it can be exploited to solve this problem.
Nov
18
comment Calculating expectation of a random variable knowing expectation of a function of it
What do you mean by "constant random variable"?
Nov
18
asked Calculating expectation of a random variable knowing expectation of a function of it
Oct
28
accepted Calculating expected value of distance in a circle-circle intersection
Oct
24
asked Calculating expected value of distance in a circle-circle intersection
Oct
24
awarded  Scholar
Oct
24
accepted A contradiction when calculating the expected value of a discrete random variable
Jul
18
asked Notation for element-wise division of vectors
Jun
22
comment Segmented area between circles
Thanks, @Victor. I do not believe if it is easy at all to formally prove that $A_{22}$ grows with distance to $t$. I think numerical evaluation of the regions (like what you did in your answer) is the best way to approach the problem. Unfortunately, I am not familiar with Mathematica; so, I am trying to implement some code in MATLAB. I will update the post if I come up with more interesting results.
Jun
21
revised Segmented area between circles
added 190 characters in body
Jun
21
revised Segmented area between circles
deleted 324 characters in body; edited title
Jun
21
comment Segmented area between circles
@GerryMyerson: Thanks for your comment. I am not sure though, given that $A_{22} < A_{12}$ when $s_2 \to \infty$, can we claim that $A_{22} < A_{12}$ for any $s_2$ between $s_1$ and $\infty$?