Question: Let X = (X 1 , X 2 ) be a two-dimensional normal random vector; E{X 1 } = 1, E{X 2 1 } =

Let X = (X₁, X₂) be a two-dimensional normal random vector; E{X₁} = 1, E{X²₁} = 5, E{X₂} = 2, E{X²₁} = 13, E{X₁X₂} = −2.

(a) Write the density of the centered vector Y = X−m, where the vector m = (1,2). Write the density of X.

(b) For t = (3,−4), (i) write the expectation, the variance and the density of t₁X₁ +t₂X₂; (ii) write the expectation, the variance and the density of the projection of X on t.

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a The covariance matrix C 512212 212 1322 Then fyx1x2 4 4 9 detC 20 and C1 1 20 exp 045x 04x... View full answer

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