Question: (a) Given the joint characteristic function of a pair of random variables, X, Y (1, 2). How do we get a marginal characteristic function

(a) Given the joint characteristic function of a pair of random variables, Φ X, Y (ω1, ω2). How do we get a marginal characteristic function of one of the random variables, say, Φ X (ω) from the joint characteristic function?
(b) Repeat part (a) for the joint PGF, H X, Y (z1, z2.

Step by Step Solution

★★★★★

3.36 Rating (177 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b xy W... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

589-M-S-C-R-V (1094).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Find the general form of the joint characteristic function of two jointly Gaussian random variables.

Let and be zero- mean jointly Gaussian random variables with a correlation coefficient of and unequal variances of 2X and 2Y. (a) Find the joint characteristic function, X, Y (1, 2). (b) Using the...

A pair of random variables has a joint characteristic function given by (a) Find E [X] and E [Y] (b) Find E [XY] and Cov (X, Y). (c) Find E [X2Y2] and E [XY3]. Px, r(@1, @z) (1- 2jw,)(1- 2jw)

The two questions in the attached pictures. Thank you. 13. Princess Aurora (better known as the Sleeping Beauty) falls asleep under the spell of Fairy Carabosse. All it takes to awaken Aurora is a...

3. [16 marks] A pair of random variables (X, Y) has a joint probability distribution in which Y has marginal probability density function fr(y) = My (1 - 4), yE ( 0, 1 ) 10, else and the conditional...

I can't wait to rate Identify the probability density function. 1 f( x ) = 9V 2n -e-(x - 20) /162, (-00, 00 ) O uniform probability density function O exponential probability density function O...

Suppose we have pair of random variables X , Y that depict the rectangular coordinates of a random point from the unit circle; i.e. the joint PDF of X, Y is _ 1/7r ,xz +312 5 1 nyOCJ) _{ 0 ,otherwise...

Can you help me to solve these two questions? Thanks 3. A pair of random variables (X , Y) has a joint probability distribution in which the marginal distribution of X is Exp(1) and the conditional...

PSTAT W120A, Summer 2016 Assignment 3.A Due Wednesday Aug. 17 Directions: Please write up your solutions and submit them on GauchoSpace by the end of the day on Wednesday. We prefer the submission to...

"I m not sure I buy what that leadership trainer is trying to sell." said Pete Fared to his colleague, Marcee McPhee. That morning. Fared and McPhee had attended a two-hour session as part of a...

Repeat Prob. 1095 assuming an isentropic efficiency of 84 percent for the turbines and 100 percent for the pumps.

CH 2 7 Master budget and planing 2 7 - 6 Computing ending accounts receivable Evans Company's cash sales are normally 6 0 % of total sales. Anticipated sales for April and May are $ 5 8 8 , 0 0 0 and...

What connection can you see between REI being a purposedriven organization and employee motivation?

According to a recent study, cell phones, especially text messaging, is the main medium for teenagers to stay connected with friends and family (CNN, March 19, 2012). It is found that only 23% of...

Henry Chow is a stockbroker working for Merrill Lynch. He knows from past experience that there is a 70% chance that his new client will want to include U.S. equity in her portfolio and a 50% chance...

The following frequency distribution shows the ages of Indias 40 richest individuals. One of these individuals is selected at random. a. What is the probability that the individual is between 50 and...

3 b. The researcher was curious whether there were differences in quiz scores for students based on which teacher they had. The results from this analysis are shown below. Provide a write-up in APA...

(10) 3. ABC Ltd. is a consumer products company selling in India and abroad. Its Balance Sheet as per Book Value and Market value are as follows: ABC Ltd (Book Value/Rs in crs) Assets Equity Debt 500...

A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b = 1.0, and they are perfectly...