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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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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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