Let y1, . . , yn be random variables with var(yi) = σ 2 and cov(yi , yj ) = rhoσ2 . the variance covariance matrix is of the form (a − b)i + bj, where a = 1, b = rho, j = 110 . therefore, in our model σ = σ 2 [(1 − rho)i + rhoj]. the inverse of this special matrix can be obtained as follows: σ−1 =

A3-dimensional figure has a square base and 4 lateral faces that meet at a point. explain the difference between the cross sections when a slice is made perpendicular to the base through the vertex, and when a slice is made perpendicular to the base and not through the vertex

Given: ae ≅ ce ; de ≅ be prove: abcd is a parallelogram. we have that ab || dc. by a similar argument used to prove that △aeb ≅ △ced, we can show that △ ≅ △ceb by. so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.

Find the volume of the solid bounded by the plane z=0 and the paraboloid z=1-x^2 –y^2