Suppose Y is an n 1 random vector, X is an n p matrix of known constants of rank p, and is a p 1 vector of regression coefficients Let Y have a N(X, 2 I) distribution Discuss the joint pdf of (X 'X) 1 X 'Y and Y ' I X(X ' X) 1 X ' Y 2

Question: Suppose Y is an n 1 random vector, X is an n p matrix of known constants of rank p, and is

Suppose Y is an n × 1 random vector, X is an n × p matrix of known constants of rank p, and β is a p × 1 vector of regression coefficients. Let Y have a N(Xβ, σ²I) distribution. Discuss the joint pdf of ˆβ = (X'X)⁻¹ X'Y and Y' [I −X(X' X)⁻¹X' ]Y /σ².

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