(c) Let (X, Y) have a Bivariate Normal distribution with parameters ux, My, ox, or, and p. Show that aX + by + c has a Normal distribution (where a, b, c are real numbers with a * 0 or b / 0). That is, any linear combination of the components of a Bivariate Normal vector is a Normal random variable. (Hint: first find the mean and variance of aX + by + c in terms of a, b, c, MX, MY, Ox, oy, and p. Then show that aX + by + c has the MGF of a normal random variable with this mean and variance. )/3. Suppose that O ~ Unif (0, 27) and V ~ Exp(1/8). Define X1 = VV cos and X2 = VV sin O. Let X = (X1, X2) be a bivariate random vector. (a) Find the distribution of the random vector X. (b) Find a scalar c such that Z = cX follows the standard bivariate normal distribution. (c) Find a lower triangular matrix A and a vector b such that b + AZ follows the bivariate normal distribution N(u, E), where 4 U = E = 9one sitting- Question 35 Which statement is supported by research on newborn taste preferences? O Newborns cannot distinguish basic tastes. The mother's diet during pregnancy has an influence on a newborn's preferences. O Newborns prefer the taste of formula to breast milk. O Unlike adults. babies relax their facial muscles in response to sour tastes. Previous ASUS Master 12 14 15 f6 X A 19 % N 3 4 5 6 7