Let X X1, X2 brvbar XN T represent an N dimensional vector of random variables that is uniformly distributed over the region, x1 x2 xN curren 1, x I yen 0, i 1, 2, brvbar N That is (a) Find the constant c (b) Find the marginal PDF for a subset of M of the N random variables (c) Are the Xi independent Are the Xi identically distributed 0, otherwise

Question: Let X = [X1, X2¦ XN] T represent an N- dimensional vector of random variables that is uniformly distributed over the region, x1 + x2

Let X = [X1, X2€¦ XN] T represent an N- dimensional vector of random variables that is uniformly distributed over the region, x1 + x2 + . . . + xN ‰¤ 1, x I ‰¥ 0, i = 1, 2, €¦ N. That is

(a) Find the constant c.
(b) Find the marginal PDF for a subset of M of the N random variables.
(c) Are the Xi independent? Are the Xi identically distributed?

0, otherwise

Step by Step Solution

★★★★★

3.24 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Define Then c I 1 N 1 Note that Using this iteration we see that T... 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 (1167).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let represent a three- dimensional vector of random variables that is uniformly distributed over the unit sphere. That is, (a) Find the constant c. (b) Find the marginal PDF for a subset of two of...

Suppose a pair of random variables is uniformly distributed over a rectangular region, A: x1 2 2

Consider a vector of random variables, X = [X1, X2. XN] T. Suppose we form a new random variable Z by performing a weighted average of the components of X. That is, Where Find the values of the...

Let X = [X1, X2, X3] T represent a three- dimensional vector of random variables that is uniformly distributed over a cubical region (a) Find the constant c. (b) Find the marginal PDF for a subset of...

Let X = [X1, X2, X,] be a 3-dimensional vector of random varialbes that is uniformly distributed over the unit sphere. That is, fx(x) = > for >+ x3+ 151. Find the marginal PDF for a subset of two of...

Let X = [X1, X2, X,]T be a 3-dimensional vector of random varialbes that is uniformly distributed over the unit sphere. That is, fx(x) = > for 12 + x3+ 1251. Find the marginal PDF for a subset of two...

Question: A company is named with your last name (e.g. Miao). It has a finance department which requires a service to be high available. You will need to 1) complete the requirement analysis (with...

Exercise 2.5. This exercise considers computer simulations of a Markov chain by using random number generators. Here, we assume that the Markov chain has a nonempty countable state space E. Let U ,...

Continue with the same setup as for Question 4. However, for this problem we are assuming asymptotic results. Let X = (X1, X2, . .., Xn ) be i.i.d. random variables from a Poisson ()) distribution....

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

A consumer has Cobb-Douglas preferences over two goods: good 1 and good 2. The consumer's preference can be represented by the utility function u(x, x) = xx where x is the amount of good 1 and x is...

A producer of home appliances is planning the production of its only electric tea kettle, known as Product Z. One unit of Product Z is made of 2 units of subassembly Y and 4 units of subassembly X....

Simulation Project 1 Excel Worksheet for Long - Term Savings Name _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ What you need to do in this project: ( 1 ) Develop an Excel spreadsheet for...

Review the hygiene factors and motivators in the two-factor theory of motivation. Do you agree with the distinction between hygiene factors and motivators? Are there any hygiene factors that you...

Suppose that you draw a single card from a standard deck of 52 playing cards. a. What is the probability that a diamond or club is drawn? b. What is the probability that the drawn card is not a 4? c....

In a large accounting firm, the proportion of accountants with MBA degrees and at least five years of professional experience is 75% as large as the proportion of accountants with no MBA degree and...

A local beer producer sells two types of beer, a regular brand and a light brand with 30% fewer calories. The companys marketing department wants to verify that its traditional approach of appealing...

initial and final block diagram for production of strong nitric acid (95%) by feedstock per annum is 1 million tonne and feed material is liquid ammonia and the calculation for the production of...

prepare an alphabetical list of all Economics majors that entered the university in 2 0 2 1 the list should only display first and last names

What's the taxable equivalent yield on a municipal bond with a yield to maturity of 6.25 percent for an investor in the 25 percent marginal tax bracket? (Round your answer to 2 decimal places.)...