78 Let (t1, , tn) denote the joint moment generating function of X1, ,Xn (a) Explain how the moment generating function of Xi , Xi (ti), can be obtained from (t1, , tn) (b) Show that X1, ,Xn are independent if and only if (t1, , tn) x1 (t1) Xn (tn) ...

The Answer is in the image, click to view ...

78. Let (t1, . . . , tn) denote the joint moment generating function of X1, .

Question:

78. Let φ(t1, . . . , tn) denote the joint moment generating function of X1, . . . ,Xn.

(a) Explain how the moment generating function of Xi , φXi (ti), can be obtained from φ(t1, . . . , tn).

(b) Show that X1, . . . ,Xn are independent if and only if

φ(t1, . . . , tn) = φx1 (t1) · · · φXn (tn)

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Probability Models

ISBN: 9780123756862

10th Edition

Authors: Sheldon M Ross

See More Books

Question Posted: Sep 16, 2024 03:01 AM

See More Questions

Calculate the binding energy per nucleon for a 14/7N nucleus.
Suppose each department in NJIT had its own database on a PC and all the PCs were on the same local area network. If we wanted to turn this into a distributed database system, which of the three...
As a 1.00-mol sample of a monatomic ideal gas expands adiabatically, the work done on it is - 2 500 J. The initial temperature and pressure of the gas are 500 K and 3.60 atm. Calculate (a) The final...
78. Let (t1, . . . , tn) denote the joint moment generating function of X1, . . . ,Xn. (a) Explain how the moment generating function of Xi , Xi (ti), can be obtained from (t1, . . . , tn). (b) Show...
Munson Manufacturing, in Gainesville, Florida, wants to arrange its four work centers so as to minimize interdepartmental parts handling costs. The flows and existing facility layout are shown in a)...
MBA 6131 Case Analysis Questions Case 1: Korea Auto Insurance Read the case and consider the following issues: 1. What is the rational for allocating central overhead to the business units? 2. What...
77. Let X and Y be independent normal random variables, each having parameters and 2. Show that X + Y is independent of X Y. Hint: Find their joint moment generating function.
Suppose in Example 2.31 that those choosing their own hats depart, while the others (those without a match) put their selected hats in the center of the room, mix them up, and then reselect. Also,...
A unity feedback system has If this system has an associated 0.5 second delay, use MATLAB to design the value of K for 20% overshoot. Make any necessary second-order approximations, but test your...
The failure rate for a high-speed fan is given by: () = (2 x 103 x 10-6)/hr where t is in hours of operation. The required design life is 100 hours. Question 14: If, by preventive maintenance, the...
calculate in detailed pls The following information relates to the banking transactions of R Brown for the month of March Year 4: CASH BOOK (Bank columns only) 2 69 Year 4 Mar 1 Balance b/d 2,370 3...
On January 2, 2018, Baltimore Company purchased 10,000 shares of the stock of Towson Company at $14 per share.Baltimore did NOT obtain significant influence as the purchase represents a 5% ownership...
Business and Management Due to the rise of other nations, the nature of competition between global companies has changed. Explain giving examples especially of America, India,China, united states
Fastnar is a large European industrial supplies company with a market capitalization of 17 billion. During the COVID-19 pandemic, Fastnar's supply chain experienced significant stress, leading to the...
A multithreaded Web server is organized as shown in Fig. 7-21. It takes 500 sec to accept a request and check the cache. Half the time the file is found in the cache and returned immediately. The...
Consider the activities undertaken by a medical clinic in your area. Required 1. Do you consider a job order cost accounting system appropriate for the clinic? 2. Identify as many factors as possible...
5. A Markov chain {Xn,n 0} with states 0, 1, 2, has the transition probability matrix?
4. Consider a process {Xn,n = 0, 1,...} which takes on the values 0, 1, or 2. Suppose P{Xn+1 = j |Xn = i,Xn1 = in1,...,X0 = i0} = PI ij , when n is even PII ij , when n is odd where 2 j=0 PI ij = 2...
3. In Exercise 2, suppose that if it has rained for the past three days, then it will rain today with probability 0.8; if it did not rain for any of the past three days, then it will rain today with...

78. Let (t1, . . . , tn) denote the joint moment generating function of X1, .

Question:

Step by Step Answer:

Introduction To Probability Models

Students also viewed these Business questions