Assume that E(H;) = 36, E(W;) = 46 and Var(H;) = Var(W;) = 4 for i = 1, 2. Let W = - W1 +W2 be an estimator of the width and H = _ H1+H2 2 be an estimator of the height of the rectangle. 2 a) [1 mark] Find the expected value and the variance of the estimator of the width. E(W) = Number (Enter the exact value) Var(W) = Number (Enter the exact value) b) [1 mark] Find the expected value and the variance of the estimator of the height. E( H ) = Number (Enter the exact value) Var(H) = Number (Enter the exact value)c) [2 marks] If we estimate the area of a rectangle via the estimator 21 = 1717 x f, determine its variance Var(1) = Number (Enter the exact value) d) [2 marks] If we estimate the area of a rectangle via the estimator H1W1 +H2W2 A2 = f calculate its variance Var(2) = Number (Enter the exact value)