A continuous random variable is said to have a Rayleigh distribution with parameter if its PDF
Question:
A continuous random variable is said to have a Rayleigh distribution with parameter σ if its PDF is given by
where σ > 0.
a. If X ∼ Rayleigh(σ), find EX.
b. If X ∼ Rayleigh(σ), find the CDF of X,FX(x).
c. If X ∼ Exponential(1) and Y = √2σ2X, show that Y ∼ Rayleigh(σ).
Transcribed Image Text:
X -x²/20² fx(x) e 02 -x²/20² {** 0 u(x) if x ≥ 0 if x < 0
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
a Finding the expected value of X The expected value of X denoted by EX is given by the following integral EX x fx dx where fx is the PDF of X In this ...View the full answer
Answered By
Ann Wangechi
hey, there, paying attention to detail is one of my strong points, i do my very best combined with passion. i enjoy researching since the net is one of my favorite places to be and to learn. i am a proficient and versatile blog, article academic and research writing i possess excellent English writing skills, great proof-reading. i am a good communicator and always provide feedback in real time. i'm experienced in the writing field, competent in computing, essays, accounting and research work and also as a Database and Systems Administrator
4.90+
151+ Reviews
291+ Question Solved
Related Book For
Introduction To Probability Statistics And Random Processes
ISBN: 9780990637202
1st Edition
Authors: Hossein Pishro-Nik
Question Posted:
Students also viewed these Business questions
-
15. The Investment Club at Bell Labs has solicited and obtained $50,000 from its members. Collectively, the members have selected the three stocks, two bond funds, and a tax-deferred annuity shown in...
-
A continuous random variable is said to have a Laplace(, b) distribution [ 14 ] if its PDF is given by
-
A continuous random variable is said to have a Pareto(x m ,) distribution [ 15 ] if its PDF is given by where x m , > 0. Let X Pareto(x m ,). a. Find the CDF of X, FX(x). b. Find P(X > 3x m |X > 2x...
-
The trial balance for Hanna Resort Limited on August 31 is as follows: Additional information: 1. The balance in Prepaid Insurance includes the cost of four months premiums for an insurance policy...
-
Environmentalists and others have long pointed out the waste caused by the excess use of paper and plastic in packaging U.S. goods. In recent years, some companies have worked to reduce the amount of...
-
Suppose we want to change the base period of the CPI from July 1983 to December 2000. Recalculate Decembers CPI for each of the years in Table 1, so that the table gives the same information about...
-
Consider a process with the following streams: When \(\Delta T_{\text {min }}=10^{\circ} \mathrm{C}\), the minimum utilities for heating and cooling are \(237 \mathrm{~kW}\) and \(145 \mathrm{~kW}\),...
-
Croftmark Co. began operations on May 1, 2010. Its Work in Process Inventory account on May 31 appeared as follows: The company applies overhead on the basis of direct labor cost. Only one job was...
-
The ideal air to fuel ratio for an engine is 14.8:1. If a vehicle burns 7 lb of fuel, how many pounds of air should it draw to achieve the ideal ratio
-
Let Z N(0, 1). If we define X = e Z+ , then we say that X has a log-normal distribution with parameters and , and we write X LogNormal(, ). a. If X LogNormal(,), find the CDF of X in terms of the...
-
A continuous random variable is said to have the standard Cauchy distribution if its PDF is given by If X has a standard Cauchy distribution, show that EX is not well-defined. Also, show EX 2 = ....
-
The following function describes the demand condition for a company that makes caps featuring names of college and professional teams in a variety of sports. Q = 2,000 - 100 P where Q is cap sales...
-
The worlds rich countries, such as the United States and Germany, have income per person that is about _____ times income per person in the worlds poor countries, such as Pakistan and India. a. 2 b....
-
Increases in the amount of human capital in the economy tend to ________ real incomes because they increase the ________ of labor. a. increase; bargaining power b. increase; productivity c. decrease;...
-
Over the past century, real GDP per person in the United States has grown about _____ percent per year, meaning it has roughly doubled every _____ years. a. 2; 14 b. 2; 35 c. 5; 14 d. 5; 35
-
Hectors General Store advertises cans of Fancy brand whole tomatoes for fifty cents per can, although he does not have any in stock. When customers arrive to buy the tomatoes, Hector tells them that...
-
If the central bank wants to contract aggregate demand, it can ________ the money supply and thereby ________ the interest rate. a. increase; increase b. increase; decrease c. decrease; increase d....
-
The partnership of Cain, Gallo, and Hamm engaged you to adjust its accounting records and convert them uniformly to the accrual basis in anticipation of admitting Kerns as a new partner. Some...
-
Repeat Exercise 16.6 using the t-test of the coefficient of correlation. Is this result identical to the one you produced in Exercise 16.6?
-
What management, organization, and technology issues would have to be addressed if a company were thinking of equipping its workers with wearable computing devices?
-
What kinds of businesses are most likely to benefit from wearable computers? Select a business and describe how a wearable computing device could help that business improve operations or decision...
-
What business benefits do cloud computing services provide? What problems do they solve?
-
What is output given the user input? >3 blind mice System.out.print("Enter info: "); Scanner keyboard = new Scanner(System.in); String info = keyboard.nextLine(); Scanner inputScnr = new...
-
Given the code below fill in the blanks. 5 => LRStack() s.push('foo') s.push('bar') s.top() s.push('baz') s.pop() s.push('bat') The stack has elements. is at the top of the stack. is second from the...
-
The following data have been extracted from the books of Alfa Ltd . Year. Sales Rs . Profit Rs 2 0 1 9 . 5 , 0 0 , 0 0 0 . ( Loss ) ( 2 5 , 0 0 0 ) 2 0 2 0 . 7 , 5 0 , 0 0 0 . 1 , 0 0 , 0 0 0 Explain...
Study smarter with the SolutionInn App