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2
votes
2answers
74 views

Conditional distribution of arrival times in Poisson process

Suppose I know over a window $[0, T)$ that I have observed $n$ samples from a poisson process $N_t \sim p(n|\lambda t) = \frac{1}{n!}(\lambda t)^{n}\exp(-\lambda t)$. What is the conditional ...
1
vote
1answer
123 views

Poisson and conditional probability

Admit that the number of participants who intend to enroll in a given training follows a Poisson distribution with a mean of $12.$ If there is not a minimum of five enrollments, training is not ...
0
votes
1answer
69 views

Poisson Process - Determining Rainfall Accumulation

Disclaimer - I'm not a statistician. Most of my knowledge on the subject is self-taught. I'm trying to grasp how continuous random variables can be used in conjunction with a discrete Poisson process....
0
votes
1answer
422 views

Calculate conditional probability for the Poisson Process

I need to calculate $P[N_{s}=k||N_{u},\,u \geq t]\,(s \leq t)$ for the Poisson process. However, I have been instructed to use the following example in order to do so: Example: The Poisson process $...
1
vote
1answer
176 views

Inter-arrival time of Poisson arrivals?

Assume a Poisson process with rate $\lambda$. Let $T_{1}$,$T_{2}$,$T_{3}$,.... be the time until the first, second, third,......(so on) arrivals following exponential distribution. If I consider ...
1
vote
0answers
243 views

Probability of a random occurrence of Poisson process to be the first occurrence

It is given, that there is an occurrence of Poisson process (at time $t$) of intensity $\lambda$ within an interval $(0, T)$. $t \in \{t_i\}; 0 < t_1 < t_2 < \cdots < t_n < T$ I need ...
7
votes
3answers
300 views

Paradox of Poisson process with at least one event in the interval

Let $X_T$ is a number of events in Poisson process of unitary rate ($\lambda = 1$) within interval of length $T$. It is known that at least one event has been observed in the interval, I want to find ...
2
votes
1answer
2k views

Distribution of inter arrival times in a Poisson process

I am new to Statistics. I am studying Poisson process, I have certain questions to ask. A process of arrival times in continuous time is called a Poisson process of rate $\lambda$ if the following ...
8
votes
2answers
566 views

Total expectation theorem for Poisson processes

I have two independent Poisson processes $A$ and $B$ with arrival rates $\lambda_A$ and $\lambda_B$, respectively. Now, the expected time for the arrival of the next item for the merged process should ...
3
votes
1answer
208 views

Poisson probability question

For part a I think its just the poisson probability of 40 with rate = 48. I'm stuck on b to d. Cars pass checkpoint A in accordance with a Poisson process at an average rate of 24 cars per hour. All ...