Suppose R is an orthogonal nn matrix. If U is an n1 vector of IID N (0,
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Suppose R is an orthogonal n×n matrix. If U is an n×1 vector of IID N (0, σ2) variables, show that RU is an n×1 vector of IID N (0, σ2)
variables. Hint: what is E(RU )? cov(RU )? (“IID” is shorthand for
“independent and identically distributed.”)
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