A random variable X has the probability-density function where Î± is an arbitrary positive constant. (a) Determine

Question:

A random variable X has the probability-density function

-ах {3 аеах, х > 0 Sx (х) %— 0, х <0

where Î± is an arbitrary positive constant.
(a) Determine the characteristic function M_x(jv).

(b) Use the characteristic function to determine E[X] and E[X²].

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

Step by Step Answer:

Related Book For book-img-for-question

Principles of Communications Systems, Modulation and Noise

ISBN: 978-8126556793

7th edition

Authors: Rodger E. Ziemer, William H. Tranter

See More Books

Question Posted: Nov 17, 2018 07:57 AM

See More Questions

The random variable X has a probability-density function uniform in the range 0 x 2 and zero elsewhere. The independent variable Y has a density uniform in the range 1 y 5 and zero elsewhere....
Three fair coins are tossed simultaneously such that they dont interact. Define a random variable X = 1 if an even number of heads is up and X = 0 otherwise. Plot the cumulative-distribution function...
A random variable X has the pdf f X (x) = Ae -bx [u(x) - u(x - B)] where u(x) is the unit step function and A, B, and b are positive constants. (a) Find the proper relationship between the constants...
A utilization greater than one suggests that the mean service time is higher than the mean inter-arrival time. True False QUESTION 3 It costs five times more money to retain a current customer than...
Which has the higher frequency: red light or blue light?
Give the outline of a task that would migrate subtasks (tasks it creates) to other systems. Include information about how it would decide when to migrate tasks, which tasks to migrate, and how the...
Enough money has been budgeted to collect independent random samples of size n, = n, = 100 from populations 1 and 2 in ordcr to estimate (pl - p2). Prior information indicates that a, = a, = 10. Have...
A diffraction grating has 4 200 rulings/cm. On a screen 2.00 m from the grating, it is found that for a particular order m, the maxima corresponding to two closely spaced wavelengths of sodium (589.0...
Jack inherits stock (a capital asset) from his brother, who died in March of 2022, when the property had a $6.7 million fair market value (FMV). This property is the only property included in his...
Marthas Wonderful Cookie Company makes a special super chocolate-chip peanut butter cookie. The company would like the cookies to average approximately eight chocolate chips apiece. Too few or too...
Consider the electron wave function where x is in nm.a. Determine the normalization constant c.b. Draw a graph of (x) over the interval -5 nm ?? x ?? 5 nm. Provide numerical scales on both axes.c....
Consider the random process of Problem 7.3. (a) Find the time-average mean and the auto correlation function. (b) Find the ensemble-average mean and the auto correlation function. (c) Is this process...
Suppose that FOIL is considering adding a literal to a clause using a binary predicate P and those previous literals (including the head of the clause) contain five different variables. a. How many...
2. Getting ready for Logarithms and Calculus! a. Fill in the chart and graph the function (I advise practicing on your scientific calculator and desmos. X f(x) = Inx 0 0.5 1 e 10...
JoJo Co. had the following balances and information for October. Beg. finished goods inventory = $30 Beg. work in process inventory = $5 Beg. raw materials inventory = $15 End. finished goods...
Subway sales have been declining since 2014. In the US, Subway has closed a number of stores due to over-expansion, outdated operations, and uninspiring menus. In Canada, Subway took a different...
Harvey Auto Parts purchased a new crane on September 1 for $35,000, paying $10,000 cash and signing a 7%, 12-month note for the remaining balance, interest to be paid at maturity. The crane is...
e4(k+1) Find the sum of the series. k = 1 8
Pick a company of your choice, go to its Annual Report for 2020, and determine the par value of its common stock.
Why can wastewater treatment requirements in Hawaii be less stringent than those in most locations on the U.S. mainland?
If E = 20e 5y (cos 5xa x sin 5xa y ), find (a) |E| at P(/6, 0.1, 2); (b) A unit vector in the direction of E at P; (c) The equation of the direction line passing through P.
For fields that do not vary with z in cylindrical coordinates, the equations of the streamlines are obtained by solving the differential equation E p /E = d/(d). Find the equation of the line...
Suppose that the Faraday concentric sphere experiment is performed in free space using a central charge at the origin, Q 1 , and with hemispheres of radius a. A second charge Q 2 (this time a point...
If the auditor believes that the financial statements prepared on the basis of the entity's income tax are not adequately titled, the auditor should : A)Issue a resignation of opinion. B)Explain the...
initial stock offering to the public. This REIT specializes in the acquisition and management of warehouses. Your firm, Blue Street Advisors, is an investment management company that is considering...
Question 3 You have been hired to run a pension fund for Mackay Inc, a small manufacturing firm. The firm currently has Gh5 million in the fund and expects to have cash inflows of $2 million a year...

A random variable X has the probability-density function where Î± is an arbitrary positive constant. (a) Determine

Question:

-ах {3 аеах, х > 0 Sx (х) %— 0, х <0

Step by Step Answer:

a The characteristic function ...View the full answer

Principles of Communications Systems, Modulation and Noise

Students also viewed these Physics questions