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Q1 Jointly Gaussian distributions (HF) 5 Points Consider the mean vector m and covariance matrix @ for the jointly Gaussian random variables X = (X1, X2 ) given below, and answer the following questions. m = C = Q1.1 Determinant of C 1 Point What is the determinant of C? O 2 O 0 3 Save Answer Q1.2 Joint pdf 1 Point Find the joint pdf fx1 ,X, ($1, x2). exp 1 (4(21 - 1)2 + {x2(21 - 1) + 4x3) O - exp - 1 (6(21 -1)2 + $12(21 - 1) + 23) O exp -(4(21 -1)2 + 4x2(x] - 1) + 4x3) O 21/2 X exp -(( -1)2 + }x2(21 - 1) + ;x3 O exp - (3(x1 - 1)2 + x2(21 - 1) + 3x3 Save AnswerQ1.3 Marginal pdf of X1 1 Point Find the marginal pdf fx, (21 ) Of expl-=(21 - 1)2} 0 - expl-3(x1 -1)2} O - exp(3x} O exp{- 3(21 - 1)' } Save Answer Q1.4 Conditional pdf of X2 1 Point Find the conditional pdf of fx, (x2 |21 )- O VB exp -1( H(21 -1)2 + 2x2(21 - 1) + 423) O _ exp - (1(21 -1)2 + 422(21 - 1) + 423) O exp - (272 (27 - 1) + 423) O 3 exp -(12(21 -1)+423) O - explo}} Save Answer Q1.5 ML estimator of X1 1 Point Find the ML (maximum likelihood) estimator of X1 given X2 (Refer class 20). 01 - 3x2 O1+ 32 O 312 O -312 O 12