Let X N3(0,) where 1 a) Showthatthespecificationabovedefinesaregularnormaldistributionon R3. b) Showthattheconcentrationmatrix K is givenas c) Letnow L
Question:
Let X ∼ N3(0,Σρ) where −1
a) Showthatthespecificationabovedefinesaregularnormaldistributionon R3.
b) Showthattheconcentrationmatrix Kρ is givenas
c) Letnow L be thesubspacespannedbytheconstantvector e = (1, 1, 1)⊤. De-
termine theprojection ΠρX onto L with respecttotheinnerproduct ⟨·, ·⟩Kρ .
d) Determinethedistributionof ΠρX and X − ΠρX.
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