Suppose the following are measurements of the temperature T (in degrees Celsius) and insects sizes S (in millimiters) T 10 20 30 5 0.2 0.1 0 S 20 0.1 0.2 0.1 80 0 0.1 0.2 (i) Find the correlation between S and T, and briefly discuss how you would interpret it. (ii) Suppose that X and Y are continuous random variables with joint density f (x, y) such that w(x) = h (y), where w (y|x) and h (y) are, respectively, the conditional and marginal density of Y. Show that COV (X,Y) = 0. (b) Consider the portfolio Rw = wR (1w) R2, where 0 < w < the return of risky asset j with expected return ; and variance 23. covariance between R1 and R2. (i) Calculate the expected return for the portfolio Rw. (ii) Determine the optimal w* that minimises the variance of Rw. [14 MARKS] 1, Rj (j = 1,2) is Let 12 denote the