3. Let (X, Y) be a random vector with p.d.f. _ 2exp{zy) if U

3. Let (X, Y) be a random vector with p.d.f. 2 y) if otherwise. Are X and Y independent? Why? Calculate Y). 4. It is suggested that the relationship between and y is the following approximate formula: The following n = 8 data values for a,' and y are observed (0, 1), (-1, 0), (1, 0.7), (-1, 0.1), (2, 0.5), (-2, -0.3), (3, 0.3), (-3, -0.3). (i) Write a linear regression model to use LSE to estimate (3. (ii) Find the distribution for b. (iii) For a given vlaue Of derive the prediction interval for y.