Suppose that Y∼N3​(μ​,Σ​) where μ=⎝⎛​212​⎠⎞​ and Σ=⎝⎛​211​130​101​⎠⎞​ Find (a) the distribution of Z1​=Y1​+Y2​+Y3​ and Z2​=Y1​−Y2​ and (b) the correlation of Z1​ and Z2​. QUESTION 7 Let Y1​ and Y2​ be independent random variables with Yi​∼N(0,1). Let [X1​X2​​]=[μ1​μ2​​]+C[Y1​Y2​​] where C:2×2=[12δ​​2δ​1​]−21​ Derive the probability density function (pdf) of [X1​X2​​].