please only answer part d, parts a,b,c have already been answered. **Multinomial Distribution Analysis**Consider random variables \(X_1, X_2, \ldots, X_{k-1}\) with a multinomial distribution:**(a)** Find the moment generating function (mgf) of \(X_1, X_2, \ldots, X_{k-2}\).**(b)** What is the probability mass function (pmf) of \(X_1, X_2, \ldots, X_{k-2}\)?**(c)** Determine the conditional pmf of \(X_{k-1}\) given that \(X_1 = x_1, X_2 = x_2, \ldots, X_{k-2} = x_{k-2}\).**(d)** What is the conditional expectation \(E(X_{k-1} | x_1, x_2, \ldots, x_{k-2})\)?

Answered: Image /qna-images/answer/129e53ee-22b8-49eb-9727-f9cdb2e00b04.jpg

Page 164, 3.1.12.* Let X₁, X2, . . ., Xk-1 have a multinomial distribution. (a) Find the mgf of X₁, X₂, ..., Xk-2. (b) What is the pmf of X₁, X₂, Xk-2? (c) Determine the conditional pmf of Xk-1 given that X₁ X₁, X₂ = x2,. (d) What is the conditional expectation E(Xk-1x1,x2,..., Xk-2)? , Xk-2 = Xk-2.

Page 164, 3.1.12.* Let X₁, X2, . . ., Xk-1 have a multinomial distribution. (a) Find the mgf of X₁, X₂, ..., Xk-2. (b) What is the pmf of X₁, X₂, Xk-2? (c) Determine the conditional pmf of Xk-1 given that X₁ X₁, X₂ = x2,. (d) What is the conditional expectation E(Xk-1x1,x2,..., Xk-2)? , Xk-2 = Xk-2.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: How many 4 letter words can be made from MATHISFUN if each word must have 2 consonants and 2 vowel

A: word : MATHISFUN consonants : MTHSFN vowels : AIU number of 4 letter word consisting 2 consonants…

Q: The password for a new online gaming site must contain three letters followed by four digits. The…

A: Given that there are 3 letters in the password and the letters can not repeat. There are 26 letters…

Q: Let X be a continuous random variable whose density is: (see image below): The probability P(0.679…

A: We have to compute the probability that x is greater than 0.679 and less than 1.177

Q: How many different license plates can be made if each is to display 3 numbers and 3 letters?

A: We have to find out no. Of ways...

Q: How many license plates consisting of three letters followed by three digits contain no letter or…

A: Here we have to find out the combination of licence plate where repetition of letters and digits…

Q: A football team scored 39 points during a game from touchdowns (6pts each) and extra points (1pt…

A: Let x be the touchdown and y be the extra points . We know that an extra point can be attempted…

Q: In a class of 200 students, 95 take geography, 115 take history and 60 take both geography and…

A: We have given that A=Geography B=History P(A)=95/200 ,P(B)=115/200 P(A and B)=60/200

Q: Given that a =(-5, 1), b = (-5, -2), and c = (-1, 1), find the number. (Round your answer to one…

A: Find your answer below

Q: The digits of a positive integer, having three digits, are in A.P. and their sum is 15. The number…

Q: Four books, one each of Geotechnical Engineering, Algebra, Trigonometry, and Calculus are to be…

Q: What are the three requirements of linear regression?

A: these are the following three requirement of linear regression

Q: A man is 6 feet tall and his shadow measures 5 feet. If the shadow of a tree near the man measures…

Q: A student must answer 6 out of 8 questions on an exam. How many different ways can he do the exam?…

A: The objective of the question is to find out the number of ways a student can answer 6 out of 8…

Q: due what questions 1-3 were already answerd wanted 3-6

Q: Jill needs to make a password for her email account. The password must be all digits and contain…

Q: Suppose a license plate contains two letters followed by three distinct digits with the first digit…

A: Ans#- Given, A license plate contains two letters followed by three distinct digits with the first…

Q: Each marble bag sold by Deshaun's Marble Company contains 5 orange marbles for every 6 green…

Q: Without expanding, show that

A: By using properties of determinant we have to show that: 1ab+c1ba+c1ca+b=0 Applying C2→C2+C3 in LHS…

Q: A realtor uses a lock to store the keys to a house that is for sale. The access code for the lock…

A: In this case, the number of ways to fill 1st digit is 9 except the digit 5.

Q: A realtor uses a lock box to store the keys to a house. The access code for the lock box consists of…

A: A permutation is the arrangement of elements. For example, three persons viz. A, B and C can be…

Question

please only answer part d, parts a,b,c have already been answered.

**Multinomial Distribution Analysis**

Consider random variables \(X_1, X_2, \ldots, X_{k-1}\) with a multinomial distribution:

**(a)** Find the moment generating function (mgf) of \(X_1, X_2, \ldots, X_{k-2}\).

**(b)** What is the probability mass function (pmf) of \(X_1, X_2, \ldots, X_{k-2}\)?

**(c)** Determine the conditional pmf of \(X_{k-1}\) given that \(X_1 = x_1, X_2 = x_2, \ldots, X_{k-2} = x_{k-2}\).

**(d)** What is the conditional expectation \(E(X_{k-1} | x_1, x_2, \ldots, x_{k-2})\)?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The access code for a car's security system consists of four digits. The first digit cannot be zero and the last digit must be even or zero. How many different codes are available?
m³ 36 ºp b) mp8
how many license plates are possible consisting of 4 letters followed by 4 digits, if the first letter must be a c? numbers and letters can be repeated.
If 20 people all shake hands with each other, how many hand shakes are there? Show all work or explain your logic in solving this problem.
A license plate used 2 digits followed by two letters. If the numbers 1 and 0 can not be used in the digits and the letter "O" can not be used as either letter, how many different license plates can be made?
The answer is not clear enough, please write in a way that can be read because I only have one try to submit.
A license plate is to consist of two letters followed by four digits. Find the number of license plates possible if the first letter cannot be Z, and repetition is permitted.
please answer letter D and the What conclusion can be drawn?
Dr. Volz gave an exam with 14 questions, but students only had to answer 10 of them. Suppose the exam instructions say that either BOTH questions 1 and 2 may be included among the ten OR NEITHER is to be included. How many different choices of 10 questions are there?