Questions relating to the Poisson point process, a description of points uniformly and independently distributed at random over some space such as the real line. The number of points within some finite region of that space follows a Poisson distribution.
Questions tagged [poisson-process]
1414 questions
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poisson process 2
Suppose that the number of vehicles passing by the stadium entrance A can be
modelled by a homogeneous Poisson process with the rate of 10 vehicles per minute, 15% thereof
being lorries and 85% being cars. Suppose that the types of particular…
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Poisson Process Continuous stochastic process
Duronto Express arrives at the Bombay Central station according to a Poisson process of rate 3 trains/hour. Local Line trains arrive according to a Poisson process of rate 4 trains/hour.
Conditionally on the event that 8 trains arrive from 9 am to…
bluelagoon
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Conditional Probability of Sum of Poisson Point Processes
I'm having trouble determining the conditional probability of the sum of two independent Poisson Point Processes, $X, Y$, with parameters $\lambda,\mu$ respectively. If $X+Y=W$, I would like to find:
$$P(W_t=w|Y_s=y)$$
where $s
scoopfaze
- 976
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Interevent Times
A Poisson Process has lambda = 0.9 What is the probability that the fourth event occurs between time 2 and time 5?
The source I'm reading has the answer pegged as 54.9%.
I got the same answer but my work is totally different, I just want to make…
Seraphim
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Question about integral change of variable in Infinite Server Queue example, Ross' Introduction to Proability Models
Picture is from Ross' Introduction to Probability Models 11th ed.
Maybe a simple question, but I'm just wondering why the second equality in (5.17) follows. I tried substituting $y = t-s$, but that gives an extra factor of $-1$.
goblinb
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Probability of Arrivals at a bank
Suppose that the probability that a given customer entering a bank is
between 50 and 70 years of age is 5/9. a.) On a given day, compute the
probability that the 7th customer entering the bank is also the 3rd
customer who is between 50 and 70…
Basileus
- 121
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Superposition of renewal processes when the interrenewal time has non-zero minimum value
I have a question concerning the superposition of renewal processes.
Assume that we have $n$ independent renewal processes with the same interrenewal time density $f(x)$ and distribution $F(x)$, both of which are known. The superposition of the $n$…
João
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How to calculate the expectation of Poisson process when its intensity is also stochastic
How to calculate the expectation of Poisson process $N_t$ when its intensity is also stochastic? Since when intensity $\lambda_t$ is non-random, then we have
$$E[dN_t] = \lambda_tdt.$$
But how about the stochastic $\lambda_t?$ I have no idea to…
user6703592
- 535
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Poisson process properties proof
i started to study about poisson process and i having a problem with the next question:
M(t) is poisson process with with parameter -x.
Ti is the first time that M(Ti)=i.
prove that (Ti+2 - Ti) has a Erlang Distribution with parameter x,k=2.
i…
Guy
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Probability in Poisson Process
Let $ {N(t)}$ be a Poisson process with $\lambda$ parameter. Let $t \in [0,T]$.
What is the probability that number of jumps in Poisson process at first half of $[0,T]$ interval will be greater than the number of jumps at second half of this…
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Is the difference between inter-arrival times in a Poisson process incrementally independent
Let $X_2$ and $X_3$ be the inter-arrival times in a Poisson process. That's $X_i = t_i - t_{i-1}$ where $t_i$ is the arrival of an event $i$. I'm trying to calculate the following probability:
$$P[X_3 - X_2 < c | X_2 < c] ..(1)$$
where $c$ is a…
cyberic
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Poisson Process Help
I've done part a and b, though a little stuck on identifying how to do the other questions. I don't really know where to look, any hints?
Patients arrive at a walk-in dental clinic according to a Poisson Process of rate 8 per hour.
(a) Find the…
blaaaaaaa
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Autocorrelation sum of poisson
Let $x$ and $y$ be independent poisson random variables with parameters $\lambda_1$ and $\lambda_2$. Let $Z=x+y$. What is the autocorrelation for $Z$ in $t_1$ and $t_2$, i.e., what is $R_Z(t_1,t_2)$?
peyman
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Probability for number of events (Poisson process)
Considering a Poisson process with intensity 2, how does one compute the probability that the total number of events in the time interval (0, 2] is exactly twice the number of events during the first half of this interval?
Jonas
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Please help me understand the following identity.
In my class we have the following equation.
$\displaystyle Pr[N(t + ∆t) − N(t) = k] = \frac{e^{\lambda\Delta t} }{ k!}$, where $k = 0, 1, 2, \ldots \quad$ $(1)$
We are talking about the poisson process. I understand what the LHS means
of $(1)$ and…
Joe
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