Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Math Expert


Home >> Math

Probability: Theory and Applications

problem 1: Suppose the arrival times of phone calls in a help centre follow a Poisson process with rate 20 per hour (so the inter-arrival times are independent exponential random variables). Management are interested in simulating the arrival process in order to decide whether to employ a new customers services representative.

(a) Use the internet or a text book to nd an ex of a congruential unit random number generator that is di fferent to the one given in the lecture notes and lab exercises.

(b) Use your random number generator to describe why random numbers generated on a computer are called `pseudo random numbers'.

(c) Use your random number generator to generate 3 unit random numbers. State what`seed' is used and describe how this can be used to repeat simulation experiments.

(d) Assuming the memoryless property and a starting time of 1pm, use your simulated unit random numbers above to generate the arrival times of the next 3 calls arriving at the centre.

problem 2: The lifetime T (in days) of an electrical component has reliability function given by: R(t) = e 0.01t for time t > 0. An electrical system consists of four such components. The system continues to function if at least one component is still `alive' and the system is repaired (by replacing all the components) when all components have expired.

(a) Find the probability density function (PDF) of T, the lifetime of a component in the system.

(b) Show that this is a valid PDF.

(c) Find the reliability function for the system.

(d) Find the probability that the system lasts for longer than 1 year (365 days).

(e) Simulate the lifetime of the system.

(f) Set the random number seed using set.seed(1). Then simulate 20 lifetimes for the system. find out the sample mean lifetime of the system using your 20 simulated values.

problem 3: A drainage system overflows into a river causing pollution when the rainfall falling in an hour exceeds 50 mm. During any given year, the maximum hourly rainfall follows an exponential distribution with mean 20 mm. Find the return period (in years) of the critical event that causes pollution in the river.

Math, Academics

  • Category:- Math
  • Reference No.:- M91465

Have any Question? 


Related Questions in Math

A collection of dimes and quarters is worth 650 there are

A collection of dimes and quarters is worth $6.50. There are 35 coins in all. How many dimes are there? Write the correct system of equations and answer in a complete sentence thank you

Problem 1determine the value of a and b for which the

Problem 1) determine the value of a and b for which the system has I. no solution II. unique solution III. infinite number of solution Problem 2) A body of mass m is in rectilinear motion along horizontal axis .the resul ...

In traveling three-fourths of the way around a circle a car

In traveling three-fourths of the way around a circle a car travels 0.224 mi. What is the radius of the traffic circle? (Do not round until the final answer. Round to the nearest thousandth as needed)

Give an on3 algorithm to find the length of the longest

Give an O(n3 ) algorithm to find the length of the longest simple path in an n-node graph, on the assumption that no cycle has a positive length. Hint : Adapt Floyd's algorithm for shortest paths (see, e.g., A. V. Aho an ...

Find the x- and y-intercepts of the line represented by the

Find the x- and y-intercepts of the line represented by the equation below. Plot both intercepts on a coordinate system and draw the line through them. 10x + 3y = 15

Spanning tree games the following figure depicts a network

Spanning tree games The following figure depicts a network of roads connecting the capital city, Washington, with three nearby towns, Bethesda, Silver Spring, and McLean. The towns are responsible for maintaining the roa ...

Exploring different businessit alignment frameworks

Exploring different business/IT alignment frameworks, methodologies and tools: Architecture: Enterprise Architecture [TOGAF] Governance: Business Performance Management [Balanced Scorecard] IT Governance [COBIT, ITIL] Co ...

What are the best ways to mitigate risk in health care

What are the best ways to mitigate risk in health care settings? Consider a focus on patient safety/satisfaction, data, and culture of the institution. Analyze at least three methods to mitigate risk, providing examples ...

Question 1 this question involves writing career goals

Question 1: This question involves writing career goals. First, write at least three five-year goals toward your career by using the guidelines within the SMART method. Remember, the SMART method involves making the goal ...

A city currently has 128 street lights as part of a urban

A city currently has 128 street lights. As part of a urban renewal program, the city council has decided to install 2 additional street lights at the end of each week for the next 52 weeks. How many street lights will th ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen