B1. (a) A random vector X = (X1, X2, X3, X4, X)' has a multivariate normal...

 

Transcribed Image Text:

B1. (a) A random vector X = (X1, X2, X3, X4, X)' has a multivariate normal distribution with mean vector and covariance matrix given by = (4, 45, 30, 35, 40)' and 1 1000 1 15 1 40 0 1540 0 4480 0 0009 Let X = (X2, X4, X5)' and X2 = (X1, X3)'. i. Determine the probability density function of X2. [4 marks] ii. If Y = write down the covariance matrix of Y. [2 marks] , X2 iii. Determine the distribution of X conditioned on X2 = (6,24)' [5 marks] B1. (a) A random vector X = (X1, X2, X3, X4, X)' has a multivariate normal distribution with mean vector and covariance matrix given by = (4, 45, 30, 35, 40)' and 1 1000 1 15 1 40 0 1540 0 4480 0 0009 Let X = (X2, X4, X5)' and X2 = (X1, X3)'. i. Determine the probability density function of X2. [4 marks] ii. If Y = write down the covariance matrix of Y. [2 marks] , X2 iii. Determine the distribution of X conditioned on X2 = (6,24)' [5 marks]