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, X3, . . .,Xk-2? (c) Determine the conditional pmf of XK-1 given that X₁ X₁, X₂ = x₂,. (d) What is the conditional expectation E(XK-11 X₁, 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
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6.
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, X3,...,Xk-2?
(c) Determine the conditional pmf of XK-1 given that X₁ X₁, X₂=X₂,
(d) What is the conditional expectation E(XK-1l X₁, X2, ..., Xk-2)?
Xk-2 = Xk-2.
Transcribed Image Text:6. 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, X3,...,Xk-2? (c) Determine the conditional pmf of XK-1 given that X₁ X₁, X₂=X₂, (d) What is the conditional expectation E(XK-1l X₁, X2, ..., Xk-2)? Xk-2 = Xk-2.
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