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Sep
12
comment Last two digits of $3^{400}$
I have seen it before, but it was not discussed in this class, which makes me think that we are supposed to do this simply using the basics of modular arithmetic?
Sep
12
asked Last two digits of $3^{400}$
Sep
9
comment Proving a non-stopping time
For $\mathbf{X} = \{X_n : n \ge 0\}$ a stochastic process, a stopping time $T$ is a random time such that for each $n \ge 0$, the event $\{T = n\}$ is completely determined by (at most) the total information known up to time n, $\{X_0, \dots, X_n\}$. I know how to informally state that $W_y$ is not a stopping time (because it depends on a time $X_n \notin \{X_0, \dots, X_{n-1}\}$ but I'm not sure how to formally prove/state this.
Sep
9
asked Proving a non-stopping time
Sep
7
comment Verifying prime factorization equivalence class
A perfect answer. Thank you.
Sep
7
accepted Verifying prime factorization equivalence class
Sep
7
asked Verifying prime factorization equivalence class
Sep
5
accepted Proving that $X_n$ is (or is not) a Markov Chain
Sep
5
comment Proving that $X_n$ is (or is not) a Markov Chain
So for $X_n=1$, should I construct a counter example where we incorrectly predict the value of $X_{n+1}$ based only on $X_n$? Showing that we need the previous two states, not just previous 1?
Sep
5
comment Proving that $X_n$ is (or is not) a Markov Chain
@AndreaColonna What are you implying about the answer?
Sep
4
comment Proving that $X_n$ is (or is not) a Markov Chain
It just occurred to me that I might try making a table of all differing values x_n+1 can assume given x_n at a certain value.
Sep
4
accepted How to show that the $k$th return to $y$ is a stopping time
Sep
4
comment How to show that the $k$th return to $y$ is a stopping time
So you mean that the event that $T_y^k$ is greater than $n$? If so, I understand thank you
Sep
4
asked Proving that $X_n$ is (or is not) a Markov Chain
Sep
4
comment How to show that the $k$th return to $y$ is a stopping time
Sorry, I'm new to Markov chains, can you clarify what you mean by this?
Sep
4
revised How to show that the $k$th return to $y$ is a stopping time
edited title
Sep
4
revised Are all compact sets in $ \Bbb R^n$, $G_\delta$ sets?
formatting
Sep
4
suggested approved edit on Are all compact sets in $ \Bbb R^n$, $G_\delta$ sets?
Sep
4
asked How to show that the $k$th return to $y$ is a stopping time
Sep
1
revised Proving that $a,n$ and $b, n$ relatively prime implies $ab,n$ relatively prime
corrected question