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22 Jan 2015: likelihood estimate of θ is (2a b)/(b 2c). 4. (a) Let X1,. ... b) For some n > 2, let X1,. ,Xn be iid with Xi Exponential(θ).

21 May 2005: 6. If A and B are subsets of Rn, we write A B for the set {a b : a A,b B}. ... Show that if Aand B are both closed and one of them is bounded, then A B is closed.

21 May 2005: 6. If A and B are subsets of Rn, we write A B for the set {a b : a A, b B}. ... Show that if Aand B are both closed and one of them is bounded, then A B is closed.

21 Nov 2007: Show that f = gR f gLand hence, or otherwise, show that f is differentiable at B. ... Show that f is differentiable at (a, b). (b) Suppose instead that D1f exists and is bounded on some open ball around (a, b), and that for fixed x.

30 Nov 2008: around (a, b), and that D2f exists at (a, b).Show that f is differentiable at (a, b).(b) Suppose instead that D1f exists and is bounded on some open ball ... around (a, b), and that for fixed xthe function y 7 f (x, y) is continuous.

29 Sep 2003: 6. If A and B are subsets of Rn, we write A B for the set {a b : a A,b B}. ... Show that if Aand B are both closed and one of them is bounded, then A B is closed.

12 Apr 2005: If B B, then fB(ω) is definedto be the value of f(φ) for any φ with φ(A) = ω(B). ... 3.1 as follows. Let K1 be the chain of all subsets of all sets B B.

29 Mar 2011: Our pointof departure is formula 6 which says there is an external isomorphism between〈A,A〉 and 〈B,B〉.(. ... We have now established that if there is an external isomorphism between〈A,A〉 and 〈B,B〉 then there is precisely one.

17 Jul 2023: a) minimize cT x subject to Ax = b. (b) minimize cT x subject to Ax b. ... d) minimize cT x subject to Ax b, x 0. In each case.

20 May 2002: 15. p. 243, lines 6 and 9: replace "(., f((r - 1)b/N /- |B_r| (b/N)2))" by "(., f((r - 1)b/N) /- |B_r| (b/N)2)". ... the brackets are misplaced). 16. p. 247, line 6: delete "<= B b3 N(-2)" (I am not quite sure here.).