Tagged Questions
0
votes
1answer
56 views
Simple Probability Matrix
Consider a simple model that predicts whether you pass you next test or not based on the result of your previous test.
If you pass your previous test, then you have 0.2 chance you will pass your ...
0
votes
1answer
37 views
Probability related to random walks in two dimensions
I'm trying to show that two random walks will eventually meet in a two dimensional setting but I can't figure out where to start. Can someone lead me towards the right direction?
0
votes
2answers
113 views
Random Walk Proof Problem
I have to do the following problem:
Let $(s_n)_{n\geq 0 }$ be a 1-dimensional, unbiased random walk. For $a,b\in\mathbb Z$, let $T_a=\inf\{n>0:s_n=a\}$ and $T_{a,b}=\inf\{n>0:s_n=a\hspace{3mm} ...
1
vote
2answers
179 views
Stopping Time, Random Walk
I'm trying to solve this problem and don't know where to start. If someone could prove it or tell me how or point me to any relevant information I'd very much appreciate it.
Let $(s_n)_{n\geq0}$ be a ...
3
votes
1answer
29 views
Infinite number of 1D-random walkers
Place exactly one random walker at each integer in $\Bbb Z$ and define $Y_n$ as the number of these who are at the origin at time n. Show that $0<\displaystyle\lim_{n\to\infty}P\{Y_n=0\}<1$ and ...
2
votes
1answer
105 views
A problem about symmetric random walk
Consider a symmetric random walk $P(X_i=1)=P(X_i=-1)=1/2$, $S_0=0$, $T_a=\min(n:S_n=a)$
We already know that $P(T_a>T_{-b})=1-P(T_{-b}<
T_a)=\frac{b}{a+b}$ and $E(\min\{T_a,T_{-b}\})=ab$.
...
3
votes
2answers
224 views
Expected value of function of random walk
I am trying to calculate $\lim_{n \to \infty} {E[e^{i \theta \frac{S_n}{n}}]}$. Where $\theta \in \mathbb{R}$, and $S_n$ is simple random walk.
I could simplify it to $\lim_{n \to \infty}E[\cos(\theta ...
0
votes
1answer
187 views
Probability mass function of a random walk process
Let $Y_n$ be a random walk process defined as
$Y_n = Y_{n-1} + X_n$; $n = 1,2\ldots$ and $Y_0 = 0$,
where $X_k = +1$ with probability $p$ and $-1$ with probability $1-p$. Write down the pmf for $Y_n$, ...
