Let X = (X1,X2)⊤ followanormaldistributionon R2 with expect-

ation 0 and covariancematrix

where a ∈ R.

a) Forwhichvaluesof a is Σ

(a) a validcovariancematrix?

b) Forwhichvaluesof a is thedistributionregular?

c) Findthedistributionof Y = (Y1, Y2)⊤ = (X1 + X2,X1 − X2)⊤ and showthat Y1 and Y2 are independent.

d) Findthedistributionof Z = Y 2 1 /3Y 2 2 .

Transcribed Image Text:

(a) = a a/2 a/2).