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Apr
16
comment Find the marginal densities of X and Y?
To prove ^, you can integrate wrt y, this this needs some tricks
Apr
9
comment Left eigenvector of stochastic matrices with eigenvalue 1
nice, are you at havard?
Apr
9
comment Left eigenvector of stochastic matrices with eigenvalue 1
I assume that eigenvalue smaller than 1 follows by the fact it is stochastic. Assume it is not, then you can contradict the fact it is not stochastic?.
Apr
8
comment Left eigenvector of stochastic matrices with eigenvalue 1
@thanasissdr i have an irreducible markov chain in mind, hence the comment about the uniqueness of equilibrium distribution.
Feb
9
comment How many pairs of positive constants $a, b$ exist such that $P(a < X < b) = 0.95$, where $X$ has a chi-squared distribution?
Infinitely many, because the support of the density function is continuous and unbounded.
Jan
1
comment Expectation of hitting time for simple symmetric random walk
to add, $S_n$ is a Markov Chain (symmetric random walk) on the integers. It is null recurrent. The proof you just gave verifies it cannot be positively recurrent.
Jan
1
comment Bound on sum random variables and Martingales
for your question, you might want to consider something like $\exp(\sigma S_n - n\phi(\sigma))$ where $\phi(\sigma)$ is the moment generating function of $X_i$. The reason being your question has something to do with $\exp$, considering this type of martingale seems appropriate.
Jan
1
comment Bound on sum random variables and Martingales
please considering accepting answers for other questions you asked
Dec
10
comment A sequence converges if and only if every subsequence converges?
It seems like no effort has been made by the OP to try to answer the question.
Nov
5
comment Limit of: $\lim_{x\rightarrow\infty}\left(\frac{x+2}{x+1}\right)^{x/2}$
Jumped way too many steps with the last equality, even with the comment. Given that the OP asked this question, I am pretty convinced he could not have filled all these gaps himself.
Nov
5
comment Limit of: $\lim_{x\rightarrow\infty}\left(\frac{x+2}{x+1}\right)^{x/2}$
still not convinced, you are saying $\lim a^b = (\lim a)^{(\lim b)}$. Your supposedly justification does not do the job.
Nov
4
comment Limit of: $\lim_{x\rightarrow\infty}\left(\frac{x+2}{x+1}\right)^{x/2}$
Not convinced by the last equality.
Oct
27
comment Binomial/Poisson distribution question
(2) and (4) are the same is my feeling too, thank you. I would like to have another confirmation before accepting this.
Oct
27
comment Binomial/Poisson distribution question
@Henry i am sorry, i am asking about (ii). I do not understand how it is different to (iv), maybe it is not. I would like an independent confirmation. I was meant to say 1,3,4 are easy...
Oct
24
comment Normal distribution tail probability inequality
nice and easy...
Oct
24
comment Normal distribution tail probability inequality
so your approach is valid for $t\geq \sqrt{\pi/2}$. i do not know how to do it, so maybe, you start by assuming otherwise.
Sep
19
comment Prove that $2^x+1$ is always greater or less than $3^\frac{x}{2}$?
please do not make edits which make the answer appears off topic.
Sep
6
comment Computing the Length of a finite length module.
Hi Sadegh. Please show us what you tried so far by editting the question. As it stands, this question fails to meet the quality of questions expected on this site.
Sep
5
comment A problem about strong law of large numbers of Shiryaev's Probability
How do you conclude from infinite mean that the series $P(|Y_i|>iR)$ diverges?
Sep
3
comment Min-max optimizacion
please write this in a more readable format.