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 \(E(X_{k-1} | x_1, x_2, \ldots, x_{k-2})\)?

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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...

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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 \(E(X_{k-1} | x_1, x_2, \ldots, x_{k-2})\)?

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