The following result is very useful

Consider a bivariate function f(x, y) such that f(1, 1) = 2000, fx(1, 1) = 9.3 and fy(1, 1) = 8.9. Estimate the value of f(2, 3) by the partial derivatives. Round your answer to 2 decimal places. Answer:b) The following result is very useful and important, and is stated only in the bivariate discrete case Let T - g( X, Y) for some function g. Then E(T) - > >g(z,y) P(X - r, Y = y) Prove this in the bivariate discrete case. stating any conditions that you require in the proof.3. Consider a bivariate normal population with ( = 0, /2 = 2,011 = 2, 022 = 1, p12 = 0.5. (a) (2 marks) Write out the bivariate normal density. (b) (3 marks) Write out the squared Mahalanobis distance (x - )"E (x - /) as a function of r] and 12. (c) (5 marks) Determine and sketch the constant -density contour that contains 50% of the probability