Suppose X = (X1, X2, . .. , Xk) ~ Multinomial(n, p) , with p = (p1, P2, ..., Pk), prove that Cov(X;, X;) = -np;p; Hint: V(X +Y) = V(X)+V(Y)+ 2Cov(X,Y)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 31E: 31. Prove statement of Theorem : for all integers and .
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Suppose X = (X1, X2,. . . , Xk)
Multinomial(n, p) , with p = (p1, P2, ... , Pk), prove that Cov(X;, X;) = –np:p;
Hint: V(X + Y) = V (X)+ V(Y)+ 2Cov(X,Y)
Transcribed Image Text:Suppose X = (X1, X2,. . . , Xk) Multinomial(n, p) , with p = (p1, P2, ... , Pk), prove that Cov(X;, X;) = –np:p; Hint: V(X + Y) = V (X)+ V(Y)+ 2Cov(X,Y)
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