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visits member for 2 years, 2 months
seen Apr 21 at 13:33

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Nov
24
comment State space reduction of a CTMC
Hi @did, I meant the equivalence was exogenous, i.e., not pertaining to the existing rates or the CTMC. The states are similar in my model, so I simply want to clump these states together and form a new CTMC (if that could be done).
Jun
8
comment Arguing on stopping time probability
@martini: Thanks, I missed out $0<p<0.5$.
Apr
7
comment Time to absorption and fraction of time spent in a state in a CTMC
@Did: Could you pl. let me know if this question needs to be edited any better?
Apr
1
comment Joint density of order statistics $f_{X_{(1)}X_{(n)}}(x,y)$ with combinatorics
@Shyam: I see... Thanks :)
Mar
30
comment Joint density of order statistics $f_{X_{(1)}X_{(n)}}(x,y)$ with combinatorics
@Did: Could you please explain the $-\dfrac{\partial^2}{\partial x\partial y}$ part? I am unable to see why that is so.
Mar
28
comment Time to absorption and fraction of time spent in a state in a CTMC
Thanks @Did. I have added some explanation. The 1st point is about expected time to absorption and the second is on expected fraction of time spent in each state prior to absorption (given an initial state).
Mar
27
comment Expected value of a variable related to uniform r.v.
@Sasha: Thanks, I have made the change.
Mar
27
comment Why is $\sum x^2 _t \times \text{Var}(\beta)=\frac{\sum x^2 _t \times \sigma^2}{ \sum x^2 _t} = \sigma^2$?
What is the context? What is $\beta$?
Mar
26
comment Intuition on Harris recurrence
@Lost1: made some changes... The wiki article was not helpful to my intuition and it has already been referred to in the question.
Mar
12
comment Dice game modelling: Lose everything on “3”, double everything on “1” or “6”
$F$ is the value function and $x$ is the earnings or the amount of money you have.
Mar
9
comment Conditional expectation in the case of $\mathcal{A}=\{\emptyset,\Omega,A,A^c\}$
@cardinal: Thanks, edited.
Mar
9
comment Let $X$ a random variable with a strictly increasing distrubution function $F_X$. Show that $Y=F_X(X) \sim \hom(0,1)$ distrubution.
$Y=F_X(X)$, so the random variable $Y$ can take values only in $[0,1]$.
Mar
8
comment How to cast the “Numberdrum” problem mathematically
@AnilBaseski: Would love to hear about them :)
Mar
7
comment Proving a matrix is positive definite using Cholesky decomposition
@user1855952: Sounds good now?
Mar
6
comment Guessing the probability by results of just 1 experiment
If you can carry out just one toss, the only definitive conclusion you can make is $X\ne 0$.
Mar
5
comment How to get transition rates in a $M/M/\infty$ queue
@Rosie: Sorry, pls. replace packets with people :) I study this from a communication networks perspective...
Mar
5
comment How to get transition rates in a $M/M/\infty$ queue
@Rosie: It is not about the number of servers, but the number of packets, which is $n$. To understand about the minimum, say you are in a state with $n$ packets and ask "When will I change from this state?" The answer for this is the minimum of the interarrival time and the $n$ service times for each of the packets.
Mar
5
comment Probablity that the drawn number is greater than the previously drawn
Which means $A_k=(x_k=1)\mid H_{k-1}$, or $A_k$ is the event of the $k^{th}$ number being the highest "given" you have observed some $k-1$ numbers before.
Mar
5
comment Probablity that the drawn number is greater than the previously drawn
I'll try to explain. $A_k$ is the event that the $k^{th}$ number is the highest of all $k$ numbers you have observed so far. Unconditionally the probability that the $k^{th}$ number is the highest is $P(x_k=1)=1/k$. But we have observed some $k-1$ numbers so far and we need $P(x_k=1\mid H_{k-1})$.
Mar
5
comment Probablity that the drawn number is greater than the previously drawn
Because when you say "than all previously drawn", what you essentially mean is "given all numbers I have observed" or in other words, "given the history so far" - this is captured by $H_{k-1}$.