56. An event independently occurs on each day with probability p. Let N(n) denote the total number...

Question:

56. An event independently occurs on each day with probability p. Let N(n)

denote the total number of events that occur on the first n days, and let Tr denote the day on which the rth event occurs.

(a) What is the distribution of N(n)?

(b) What is the distribution of T1?

(c) What is the distribution of Tr ?

(d) Given that N(n) = r, show that the set of r days on which events occurred has the same distribution as a random selection (without replacement) of r of the values 1, 2,...,n.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Probability Models

ISBN: 9780080467825

9th Edition

Authors: Sheldon M Ross

See More Books

Question Posted: Sep 14, 2024 07:01 AM

See More Questions

A company conducts a Security model workshop to review configuration options. The company uses Microsoft Entra ID to control access and permissions within multiple corporate applications. When users...
Chatterjee is an executive with XYZ Corp. In 2015, XYZ gave Chatterjee 1,000 nonqualified stock options, each with an option price of $60, when the price of XYZ stock was $80. In 2016 Chatterjee...
Record Sales Gross and Net On June 3, Bolton Company sold to Arquette Company merchandise having a sale price of $2,000 with terms of 2/10, n/60 f.o.b. shipping point. An invoice totaling $90, terms...
56. An event independently occurs on each day with probability p. Let N(n) denote the total number of events that occur on the first n days, and let Tr denote the day on which the rth event occurs....
Comparative financial statements for Weaver Company follow: During 2009, the company sold some equipment for $20 that had cost $40 and on which there was accumulated depreciation of $16. In addition,...
content area top Part 1 Precision Camera Services started the year with total assets of $130,000 and total liabilities of $60,000. The revenues and the expenses for the year amounted to $150,000 and...
57. Events occur according to a Poisson process with rate = 2 per hour. (a) What is the probability that no event occurs between 8 P.M. and 9 P.M.? (b) Starting at noon, what is the expected time at...
55. Consider a single server queuing system where customers arrive according to a Poisson process with rate , service times are exponential with rate , and customers are served in the order of their...
Consider the two differential equations each having the critical points a, b, and c; suppose that a < b < c. For one of these equations, only the critical point b is stable; for the other equation, b...
The Situation: During the wedding reception of Jeremy and Megan Fielding at the Fielding family mansion, Blake Rosewood, a guest at the wedding, ran yelling into the main ballroom, having discovered...
Final Assignment (To be completed by the student) 1. Briefly describe the ISD process, compare and outline the components. (200 words - 4 marks) Given the Needs Analysis provided by the company to...
An automated, swinging security light, hanging from the corner of a 35 ft tall building, is lighting the ground in front of the building. The angle 0 (see image below) is increasing at a rate of 0.6...
A department has three machines. The following figures indicate the departmental expenses for the most recent month Depreciation of machinery Depreciation of building Repairs to machinery Insurance...
In this module, you will plan a diving trip. You will need to know estimates of the pressure changes that you will experience. For example, if you estimate reaching depths of 200 ft (61.0 m). The...
Given the waveform shown, determine the type of symmetry that exists if the origin is selected at: (a) l1 and (b) l2.
An access route is being constructed across a field (Figure Q8). Apart from a relatively firm strip of ground alongside the field's longer side AB, the ground is generally marshy. The route can...
33. Prove the combinatorial identity ;:0-0)-G:.)(:) (a) by induction on / (b) by a backwards induction argument on /that is, prove it first for / = , then assume it for / = k and show that this...
32. For the model of Section 9.7, compute (i) the average up time, (ii) the average down time, and (iii) the system failure rate for a k-out-of-n structure.
31. Show that the variance of the lifetime of a k-out-of-n system of components, each of whose lifetimes is exponential with mean 0, is given by 2 -k

56. An event independently occurs on each day with probability p. Let N(n) denote the total number...

Question:

Step by Step Answer:

Introduction To Probability Models

Students also viewed these Business questions