Question: If show that (a) E[X 2n ] = 1 · 3 · 5 ··· (2n - 1) Ï 2n , for n = 1,2,... (b)

If

fx(x) -(2π σ') exp 2σ2

show that 

(a) E[X2n] = 1 · 3 · 5 ··· (2n - 1) σ2n, for n = 1,2,...

(b) E[X2n-1] = 0 for n = 1,2,...

fx(x) -(2 ') exp 22

Step by Step Solution

★★★★★

3.49 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a The integral evaluates as follows where y x 2 12 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Principles Communications Systems Questions!

Q:

A car is traveling along the 45o line in S (Fig. 12.25), at (ordinary) speed (2/??5)c. (a) Find the components ux and uy of the (ordinary) velocity. (b) Find the components x and y of the proper...

Q:

(a) The cross-section Ï(udÌ W + ) near the mass of the W + is given by a BreitWigner formula (3.34b). For Ï(udÌ W + ) this may be written as where (M,Î) are the mass and...

Q:

The hydrogenbromine reaction corresponds to the production of HBr(g) from H 2 (g) and Br 2 (g) as follows: H 2 (g) + Br 2 (g) 2HBr(g). This reaction is famous for its complex rate law, determined by...

Q:

1. Determine the convergence or divergence of the sequence with the given nth term. Show your work. [5 pts each] a. a = 2n +3 5n b. a, = 4n- +1 2. Determine the convergence or divergence of the...

Q:

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

Q:

Math 2242 Final Project Spring 2015 Due Date: 11:59 pm, May 5, 2015 Instructor: Jianqiang Zhao The Honor Code: On my honor, I will be academically honest in all of my course work and will not...

Q:

PLEASE HELP WITH THSES CALCULUS QUESTIONS. SHOW ALL WORK!!! D Find a power series representation for the function and determine the interval of convergence f ( X = XI *4 + 15 () Evaluate the...

Q:

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

Q:

t Bo 2 ot q-q Qo Section 11.10 The Maclaurin series for f'(x) is given by Zio(l)"mgn. Use integration to find the Maclaurin series for f(z) such that f(0) = 0. Section 11.10 Use multiplication of...

Q:

6. DIRECTIONS. In the sequence 9, 18, 27, 36, 45, 54, 63, 72, ..., determine the following. Write your answers on the space provided before each item. 1. a4 2.a6 3. a1 4. a7 5. a3 C. DIRECTIONS:...

Q:

ASC REFERENCE NUMBER PLS. The Sherwin Williams Company filed its Form 10-K for the fiscal year ended December 31, 2019 with the SEC on 2020-02-21. The Notes to the Financial Statements in Item 8 of...

Q:

A structured walkthrough penetration test of a fictional company, Artemis, Incorporated (Artemis). A structured walkthrough is an organized procedure for a group of peers to review and discuss the...

Q:

15.42 The following table contains the observed distribution of the last digit of the forecasted high temperature on December 10, 2000, for n 5 150 U.S. and international cities. (Source: New York...

Q:

Discuss the problems you see in comparing the GDPs of two countries, say, the United States and the Peoples Republic of China.

Q:

A small child gives a plastic frog a big push at the bottom of a slippery 2.0-m-long, 1.0-m-high ramp, starting it with a speed of 5.0 m/s. What is the frogs speed as it flies off the top of the ramp?

Q:

FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v 0x = 8.0 m/s at t 0 = 0 s. What is the particles velocity at t = 4.0 s? Figure...

Q:

FIGURE EX2.32 shows the acceleration graph for a particle that starts from rest at t = 0 s. What is the particles velocity at t = 6 s? Figure Ex 2.32 a, (m/s?) 10- 5- 0- -t (s) 2

Q:

8.3 The accountant of your business has recently been taken ill through overwork. In his absence his assistant has prepared some calculations of the profitability of a project, which are to be...

Q:

Below, you will find Treasury Bond quotes. To calculate the number of years until maturity, assume that it is currently May 2013. Rate maturity (mo/yr) Bid Asked Chg Ask Yld ?? May 19 103.5592...

Q:

Given the following term structure, what is the forward rate of a 3-year treasury bond issued 1 year from now? What is the forward rate of a 2-yeat treasury bond issued 3 year from nowipiease answer...