2) Consider the following joint probability density function 1 f(x, y) = = e 2(1-2) (x-2pxy+y)...

Transcribed Image Text:

2) Consider the following joint probability density function 1 f(x, y) = = e 2(1-2) (x-2pxy+y) 3 x,yR, p-1, 1]. 2 1-p A special case of the bivariate normal distribution centered at (x, y) = (0, 0), with component variances (0, 0) = (1, 1) and correlation parameter p. (a) Write an R function that computes f(x, y) for any value of x, y and p. (b) Plot (a) with p = 0 for x [3, 3] and y [3,3]. Use light blue, values of phi and theta of 30 and add "f(x,y)" as a label for the z axis. (c) Using (b) plot with phi = theta = i, i = 0, 10, 20, 30, ..., 100. Do this in a for loop with a pause of one second between each plot. Hint: Use R's help on Sys.sleep(). (d) Repeat (b) with p = -0.8, -0.5, 0.0, 0.5, 0.8. What do you observe? (e) Plot f(x, 1) on x = [-3,3] with p = 0. What does this curve look like to you? (f) Plot f(1,y) on y [3, 3] with p = 0. 2) Consider the following joint probability density function 1 f(x, y) = = e 2(1-2) (x-2pxy+y) 3 x,yR, p-1, 1]. 2 1-p A special case of the bivariate normal distribution centered at (x, y) = (0, 0), with component variances (0, 0) = (1, 1) and correlation parameter p. (a) Write an R function that computes f(x, y) for any value of x, y and p. (b) Plot (a) with p = 0 for x [3, 3] and y [3,3]. Use light blue, values of phi and theta of 30 and add "f(x,y)" as a label for the z axis. (c) Using (b) plot with phi = theta = i, i = 0, 10, 20, 30, ..., 100. Do this in a for loop with a pause of one second between each plot. Hint: Use R's help on Sys.sleep(). (d) Repeat (b) with p = -0.8, -0.5, 0.0, 0.5, 0.8. What do you observe? (e) Plot f(x, 1) on x = [-3,3] with p = 0. What does this curve look like to you? (f) Plot f(1,y) on y [3, 3] with p = 0.