(5/5)

Hire Me
(5/5)

Hire Me
(5/5)

Hire Me
(5/5)

Hire Me
(5/5)

A new startup company has developed a top-of-the line wind turbine for generating electricity.

INSTRUCTIONS TO CANDIDATES

1.

A new startup company has developed a top-of-the line wind turbine for generating electricity. The company provides the following reliability assurances: The time (in years) until first failure of the system, is given by random variable X which is distributed according to

1

fx (x) = u(x − 1)

where u(·) is the standard unit step function. Evidently, there is no failure in the first year, which is of course covered by warranty...

The first failure is usually repairable so the system can be put back into service, and the company provides further assurances. Let random variable Y denote the overall lifetime of the system (where, clearly, Y > X). It has been established that when X takes the value x, the system overall lifetime Y is distributed according to x/y2, for y≥ 2. Find:

a) The joint density fxy(x, y) and the marginal density of the system overall lifetime fr (y).

b) The conditional density of the time to first failure, given the system overall lifetime: fxy (xy).

c) The probability that the overall lifetime will be at least three times the period until first failure, i.e., PY > 3X].

2. A Powerful detector measure the frequency of radiation

virtually the entire electromagnetic spectrum, ranging from 1 kHz (extremely low frequency radio waves used to communicate with submarines) through the visible spectrum, and all the way up to frequencies of over 1020 Hz (Gamma rays). Let random variable Z be the frequency measured in kHz. Its PDF is:

「z(2) = au(2 (-1) -1),

where u(·) is the standard unit step function.

a) The wavelength is given by random variable Y = cZ-1, where constant e denotes the speed of light (in appropriate units). Find its PDF, fy (y).

b) Given the extensive electromagnetic spectrum, it is often useful to plot the frequency measurements in log scale. Let X = log(Z), and find its PDF, fx(x).

c) Are X and Y uncorrelated and/or independent? Prove your answer mathematically, and explain why it should have been expected.

(5/5)

Related Questions

. The fundamental operations of create, read, update, and delete (CRUD) in either Python or Java

CS 340 Milestone One Guidelines and Rubric  Overview: For this assignment, you will implement the fundamental operations of create, read, update,

. Develop a program to emulate a purchase transaction at a retail store. This  program will have two classes, a LineItem class and a Transaction class

Retail Transaction Programming Project  Project Requirements:  Develop a program to emulate a purchase transaction at a retail store. This

. The following program contains five errors. Identify the errors and fix them

7COM1028   Secure Systems Programming   Referral Coursework: Secure

. Accepts the following from a user: Item Name Item Quantity Item Price Allows the user to create a file to store the sales receipt contents

Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip

. The final project will encompass developing a web service using a software stack and implementing an industry-standard interface. Regardless of whether you choose to pursue application development goals as a pure developer or as a software engineer

CS 340 Final Project Guidelines and Rubric  Overview The final project will encompass developing a web service using a software stack and impleme