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Bonus 2.(2') Suppose that a discrete random vector X = (X1, X2, X3) follows multinomial distribution with parameters n and (P1, P2, P3). (a) Let U = X₁, V = X2 + X3, what is the distribution of (U,V)? (b) What is the conditional distribution of (X1, X2)|X3 = x3?

Bonus 2.(2') Suppose that a discrete random vector X = (X1, X2, X3) follows multinomial distribution with parameters n and (P1, P2, P3). (a) Let U = X₁, V = X2 + X3, what is the distribution of (U,V)? (b) What is the conditional distribution of (X1, X2)|X3 = x3?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Bonus 2.(2') Suppose that a discrete random vector X = (X1, X2, X3) follows multinomial distribution with parameters n and (P1, P2, P3). (a) Let U = X₁, V = X2 + X3, what is the distribution of (U,V)? (b) What is the conditional distribution of (X1, X2)|X3 = x3?
Transcribed Image Text:Bonus 2.(2') Suppose that a discrete random vector X = (X1, X2, X3) follows multinomial distribution with parameters n and (P1, P2, P3). (a) Let U = X₁, V = X2 + X3, what is the distribution of (U,V)? (b) What is the conditional distribution of (X1, X2)|X3 = x3?
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