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8 Mar 2022: 1. Let X Exp(λ). (a) Find P(a < X < b) for 0 < a < b. ... X -1 0 1Y. -1 a b c0 d e f1 g h i.

24 Oct 2022: Prof. Dr. B. Löwe. Example Sheet #2. (15) Work over the alphabet Σ = {0, 1} and for n 1 consider. ... Prove that L(G) = L(a+). (19) Consider the regular grammar G = (Σ, V, P, S) with P = {S cS, S cA, A aA, A aB, B bB, B b}.

28 Nov 2022: You may assume that A and B can be triangulated so that A B is asubcomplex of both A and B. ... Show that the linear map A : R2 R2preserves the equivalence relation (a, b) (a′, b′) (a a′, b b′) Z2, andso induces a continuous map fA : T.

6 Jul 2022: Forexample if a,b C and x,y,z V , then. (x,ay bz) =1. ... Then (Pa,Pb) = 〈a,b〉 for a,b V. So, for each g G,.

7 Oct 2022: From Riesz representation Theorem, there exists T(x′) Hsuch that. 〈x′,T(x)〉B′B = (x | T(x′))H for all x H. ... AB be a converging sequence, then zn = anbn z and by compactness ofA: aφ(n) a implies bφ(n) za b B since B is closed, and hence z