Some Special Distributions 198 3.5 The Multivariate Normal Distribution In this section we present the multivariate normal distribution. In the first part of the section, we introduce the bivariate normal distribution, leaving most of the proofs to the later section, Section 3.5.2. 3.5.1 Bivariate Normal Distribution We say that (X, Y') follows a bivariate normal distribution if its pdf is given by (3.5.1) 270102\\/1 -p2 2 1/7, -DO 0, for i = 1, 2, and p satisfies p' 0, the points of equal probability (or density) are given by {(r, y) : /(x, y) = c}. It follows with some algebra that these sets are ellipses. In general for multivariate distributions, we call these sets contours of the pdfs. Hence, the contours of bivariate normal distributions areQUESTION & Consider the following bivariate function: f (1,X, ) = 2xx, +1, x, >0, x, >0 Which of the following equations describes the level curves, or contours, for this function? O xX, = c, c>1 O 1 =- ,C > O C c>0 O G = -, c>1Question 24 1 pts Marching cubes is a method for computing the contour of a bivariate function. O True O False Question 25 1 pts Marching squares is a method for computing the contour of a bivariate function. O True O False Question 26 1 pts Height maps are an effective tool for visualizing trivariate functions. O True O False1. For a bivariate distribution with the following joint pdf 0 2Y) 2. Repeat with f(x, y) = exp(-x) r>y>0 3. A random variable X has the following pdf: 3c when -1