SST 304 • UNIT 4 • Statistics
Determination Of Parameters Of Mvn Distribution
Topics covered: Objectives, Obtain the components of the mean vector from the quadratic form in the
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Verified Examination Problems
5 verified questions in catalogQuestion 1 (13 marks)
For the bivariate normal density (f(x_1,x_2)=c\exp\left{-\frac{1}{2}Q\right}), where (Q=4x_1^2+x_2^2-2x_1x_2), determine:
(i) the dispersion matrix (\Sigma), and hence obtain the value of the constant (c);
(ii) the marginal density of (X_2);
(iii) the conditional density of (X_1) given (X_2=x_2);
(iv) the expected value of (Q).
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Question 2 (4 marks)
b) Obtain the marginal density of $(X_1, X_3)$ [4 marks]
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