Question: Question 9: By identifying the terms that are linear and quadratic with respect to p() in the exponential factor of f(p()|z()), show that the mean

Question 9: By identifying the terms that are linear and quadratic with respect to p() in the exponential factor of f(p()|z()), show that the mean and covariance matrix of f(p(t) |z(t) ) are given by milt = mult-1+ K+z(t) Ett = (12 - Ktc ) Ent-1 (8) with z (t) _ z (t ) - cmit-1 Kt = ( Ett-10) /82 B2 = cEnticton and 12 the 2 x 2 identity matrix. (6 Marks) Useful formula: Sherman-Morrison formula Suppose W E Rnxn is an invertible square matrix and u, v E R" are column vectors. Then Wuv invertible if and only if v W-lu * -1 and (W +uv ) 1 = W-1_ W -luvTW-1 1 +v W-lu (9)

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