2) Consider the following joint probability density function1f(r, v) = a ), 1,y € R, p E [–1,1).27 V1- p221- (22–2pxy+y?)x, Y E R, p E [–1, 1].A special case of the bivariate normal distribution centered at (µx, µy) = (0, 0), withcomponent variances (o,o3) = (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 E [-3,3] and y E [-3,3]. Use light blue, values of phiand 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 loopwith 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 E [-3,3] with p= 0. What does this curve look like to you?(f) Plot f(1,y) on y E [-3, 3] with p= 0.Submit your R code as q2.R using the same conventions as question 1).

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following joint probability density function 1 f(x, y) ²2-2pzy+s"), x,y € R, p E [-1, 1]. 27/1 A special case of the bivariate normal distribution centered at (µx, µy) = (0,0), with component variances (ož,o3) = (1, 1) and correlation parameter p.