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-1|×1,×2, • • •, 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-1|×1,×2, • • •, Xk-2)? Xk-2 = Xk-2.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Please answer page 164 3.1.12.
Transcribed Image Text:Page 164, 3.1.12.* Let \( X_1, X_2, \ldots, X_{k-1} \) have a multinomial distribution.
(a) Find the mgf of \( X_1, X_2, \ldots, X_{k-2} \).
(b) What is the 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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