Answer Happy

= Let X = [X2, X2] be a bivariate Normal random variable with: Mean matrix: j = E[X] = [2.2]; and Covariance matrix: E = E[CX – {)(X – w)"= [0.6 09] 0.61 (iii) Using mvnpdf () function, plot the bivariate normal probability density function of X over an appropriate range along both dimensions. • Find the peak values of 2D pdf surface plot. . Find the total volume under the 2D pdf surface plot. (iv) Using mvncdf () function, plot the bivariate normal cumulative distribution function of X over an appropriate range along both dimensions. . Find the value of 2D cdf at mean point i.e., at (2,2). . At what point(s), the 2D cdf value is equal to 0.5? (v) Using mvnrnd () function, generate 106 cases of random numbers from bivariate normal distribution with parameters given above . Using the generated sample, estimate the probability of the event {(1 < X < 3), (2 < X < 4)). Hint find() and numel(). - Verify the P{(1 < X < 3),(2 < X < 4)} using mvncdf(). Hint: y = muncdf (xl, xu, mu,SIGMA) returns the multivariate normal cumulative probability evaluated over the rectangle with lower and upper limits defined by xl and xu. • Verify the P{(1 < X < 3),(2 < X < 4)} using mvnpdf (). Hint: The probability that a point (x1, x2) will assume a value in a region R can be found by integrating the bivariate probability density function over the region. R