- = Suppose that the joint distribution function of (U,V) is given by the Farlie-Morgenstern copula: Pr[U

Suppose that the joint distribution function of (U, V) is given by the Farlie-Morgenste copula: uv[l + 0(1 u) 1 v)] Pr[U u, v v] COL, v) where 101 1 is a parameter and u, v e [0, 1]. (a) Compute the Pearson's correlation p Cor(U, V). (b) Compute the Spearman's correlation given by ps 12 v) uv)dudv. 0 implies that U and V are (c) Show that for the FM-copula, p 0 or ps independent.