Question: 15. Show that if N(t) : t 0 is a Poisson process, the conditional distribution of the first arrival time given N(t) =

15. Show that if



N(t) : t ≥ 0


is a Poisson process, the conditional distribution of the first arrival time given N(t) = 1 is uniform on (0, t).

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Probability And Stochastic Modeling Questions!

Q:

As David Robinson works his way through the large, festive crowd, he keeps bumping into people he knows. All the while, Robinson is hoping that he will avoid the one person he doesn't want to meet...

Q:

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Q:

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Q:

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

Q:

12. Show that if $ N (t): t 0 % is a Poisson process, the conditional distribution of the first arrival time given N (t) = 1 is uniform on (0, t).

Q:

10. In data communication, messages are usually combinations of characters, and each character consists of a number of bits. A bit is the smallest unit of information and is either 1 or 0. Suppose...

Q:

show all explanations for all questios please 4. Let {X (1).1 2 0) be a Poisson process with rate A. Let T. denote the arrival time of the nith event. (a) Find E[Tm], the expected arrival time of the...

Q:

Hi, it's me again Thanks for helping me with the answer last time d u 1. (a) Let Y1, Y2, ..., Yn be a random sample from a Bernoulli (p) distribution (i.e. Binomial(1, p)). Show ELI K is a minimal...

Q:

C# - In this assignment, you will develop and implement a discrete simulator (single-threaded) that implements a five-level multilevel feedback queue. A feedback queue is a technique used in...

Q:

Consider a conditional Poisson process where the distribution of A is the gamma distribution with parameters m and a that is, the density is given by - g(A) = aea (a)/(m 1)', 0

Q:

Question: Track down the basic point(s) for directing a theory test on the mean with a2 obscure for (a) left-followed test with n = 25; a = .05 (b) left-followed test with n = 150; a = .10 (c)...

Q:

Bienestar Inc., has the following departmental structure for producing a well-known multivitamin: A consultant designed the following cellular manufacturing structure for the same product: The times...

Q:

Azulene, an isomer of naphthalene, has a remarkably large dipole moment for a hydrocarbon (? = 1.0 D). Explain, using resonance structures. Azulene

Q:

The three main categories of foreign exchange risk a company faces are _ _ _ _ _ _ _ _ . Question 7 options: economic risk, business risk, and exposure risk exposure risk, fluctuation risk, and...

Q:

In the article by P. Ridker et al. titled "A Randomized Trial of Low-dose Aspirin in the Primary Prevention of Cardiovascular Disease inWomen" (New England Journal of Medicine, Vol. 352, pp....