Tagged Questions
-1
votes
0answers
23 views
Random process x(t) =C and C is uniform over [-2,3]
I need reassurance that if I do a a few sample realizations of this random process they are all going to look the same. They are going to be an horizontal line with x(t) constant equal to 1/5.
I see ...
0
votes
1answer
67 views
The variance of a simple random walk/process
I've been trying to wrap my head around this for the past day. Please help!
Let $\epsilon_i = \pm 1$ with equal probabilities independently for $i=1,...,N$.
Then $Z_i = \epsilon_1 + ... + \epsilon_i$ ...
7
votes
1answer
153 views
Repeatedly Toss Balls into Bins
$n$ balls are randomly tossed into $m$ bins, each bin can hold $k$ balls. If a ball is tossed into a full bin (already has $k$ balls in it), it can be tossed repeatedly and randomly into the $m$ bins ...
2
votes
2answers
85 views
Probability of a Specific Run Occurring in a Random Process
A random process has three possible outcomes: $A$, $B$, and $C$. At each step, the outcome is decided randomly, and is uncorrelated with previous outcomes. The outcomes occur with probabilities $p_A$, ...
2
votes
1answer
185 views
Markov process vs. markov chain vs. random process vs. stochastic process vs. collection of random variables
I'm trying to understand each of the above terms, and I'm having a lot of trouble deciphering the difference between them (note, my mathematics training isn't very strong - so please go easy on the ...
0
votes
0answers
31 views
Difference between kappa and delta in mixed-effects model
(This question is a crosspost from Cross Validated)
I have a following stochastic model describing evolution of a process (Y) in space and time. Ds and Dt are domain in space (2D with x and y axes) ...
0
votes
2answers
49 views
Given a random sequence of input points does it always produce a random output, excluding f(x) = constant?
Assume I have $y = f(x) \ne \mathrm{constant} $ and $(x_1 , \ldots ,x_N)$ a sequence N random input points, is there a set of criteria or a theorem that tells me that the output sequence $(y_1, ...
0
votes
0answers
207 views
jointly stationary random process
If two wide-sense stationary processes $X(t)$ and $Y(t)$ are uncorrelated, then the cross correlation is
$R_{XY}(t_1,t_2) = E\{X(t_1)Y(t_2)\} = E\{X(t_1)\}E\{Y(t_2)\}$,
which will be a constant, ...
0
votes
0answers
554 views
Pseudo-random binary sequence generated by shift register
Binary sequence generated by shift register with feedback have periodic properties. A simple 4-bit shift register shown in Fig (a). For the initial condition shown, it can be verified that the ...
1
vote
1answer
86 views
The probability of a discrete-time random process ever incurring a certain drop from “peak to bottom”
Background. Let $Y_1,Y_2,\ldots$ be i.i.d. random variables such that
$$P(Y_i<-1) = 0,$$
$$P(Y_i<0) > 0,\quad P(Y_i>0)>0,$$
$$E[Y_i] = \mu > 0\qquad \text{($\mu$ is finite)}.$$
Now ...
4
votes
3answers
2k views
What's the difference between stochastic and random?
What's the difference between stochastic and random? I've read in the portuguese wikipedia that there's a difference, but I still didn't see this point on english wikipedia.
2
votes
2answers
159 views
Are probabilities proportional to the distance traveled in a random walk? What if the initial position is a bit biased?
A marker is placed at zero on the number line and a fair coin is flipped. On each flip we move one unit to the right. If it lands on heads, the marker is moved one unit up. If it lands on tails, the ...
3
votes
1answer
197 views
what's the difference between RDE and SDE?
what's the difference between random differential equation and stochastic differential equation?
does stochastic differential equations include random differential equation?
