Question: Let {N(t), t>=0} be a Poisson process with rate lambda. Let Sn denote the time of the nth event. Find: a) E [S4] b) E

Let {N(t), t>=0} be a Poisson process with rate lambda. Let Sn denote the time of the nth event. Find:

a) E [S4]

b) E [S4 | N(1) =2]

c) E [N(4) - N(2) | N(1) =3]

explain how you solve this and show every step for each part

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 Mathematics Questions!

Q:

Let [N(), 0] be a Poisson process with rate 1. Let S,, denote the time of the nth event. Find (a) E[S4] (b) E[S, N(1) (c) E[N(4) 2] N(2) N(1) = 3]

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:

Inventory model I: A retailer sells headphones one at a time according to demand which forms a Poisson process at rate \ lambda : At Poisson arrival time tn ( n th demand request ) , the inventory...

Q:

23. Let X(t) be a Poisson process with rate . (a) Use words to justify that the events [X(t) = 1] [X(1) = 1] and [X(t) = 1] [X(1) X(t) = 0] are the same (b) Use Proposition 3.4-2 to find the...

Q:

let (N., +>=0) be a poisson counting process with rate A = 2, and define t,=10, t2=18, n,=4, n2=10. a) Determine P( M = n1, Nez = n2) b) Determine P( N (1, ti] = n1, N(t1 - 1, to] = n2) c)Determine...

Q:

10.13 Let Xt, t 0, be a Poisson process of rate . Let T0 = 0, and let Ti be the time of the ith observation (jump of X), if i 1. Let N = inf{k 1 : Tk Tk1 > 1}. Find ETN , EN, and E(TN |N = 8).

Q:

Explain how to derive a sequence of transformations to achieve the overall effect of performing a 2D rotation about an arbitrary point. Discuss the problems of providing tractable models of...

Q:

e SRAM banks be efficiently interconnected so that the cache's access time is constant regardless of which bank is accessed? [4 marks] (d) Why might it be advantageous to be able to manage the amount...

Q:

What is a function calling convention and how does it impact the design of the RISC-V instruction set architecture (ISA)? [4 marks] (d) Consider the following C function that computes the greatest...

Q:

1)Dr. Turner is reviewing her patient notes from the visits she had today. However, she is on-call and will receive pages that require immediate attention. Pages come at a Pois- son rate of 4 pages...

Q:

Please answer all questions 13. Which of the following statements about cancer is (are) false? Viruses can cause some cancers. (a) (b) (c) Tobacco use is responsible for more than 20% of all cancer...

Q:

You are the Human Resources manager for a large food processing company and have the responsibility for hiring new employees. When interviewing two prospective employees for positions to bag salad...

Q:

what is the R squared for both machine hours and labor hours

Q:

Which of the following statements is FALSE? In - transit inventory costs do not vary by stock protection level Rail rates are generally lower than Motor Carrier freight rates Stockout costs do not...

Q:

If you were a human resource manager responsible for improving cooperation and communication between employees (who come from different cultural backgrounds but who work together in teams in your...

Q:

Does the expansion of international trade benefit everybody? Does it matter if it does not?

Q:

Evaluate the evidence and arguments concerning the fairness of the economic impact of world trade liberalisation.