Suppose the multivariate random variables (Z1, Z2, Z3) have a standard Gaussian distribution on R3. Let the larger eigen

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Suppose The Multivariate Random Variables Z1 Z2 Z3 Have A Standard Gaussian Distribution On R3 Let The Larger Eigen 1 (130.38 KiB) Viewed 104 times

Suppose the multivariate random variables (Z1, Z2, Z3) have a standard Gaussian distribution on R3. Let the larger eigenvalue of the matrix “ 1221 Z3 V22, be 11 and the smaller one is called 12. (a) [2 mark] Find a formula for 11 and 12 in terms of Z1, Z2, Z3. (b) [1 mark] Define random variables X and Y by X = 11 + 12 Y = 1 -12. Write down the formula for X and Y in terms of Z1, Z2, Z3. (c) (7 marks] Find the density function of [You should explicitly calculate any unknown constants.] (d) (4 marks] Find, for c> 1, the probability P (^> cl2).