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Use the elimination method in Exercises 55 – 58 to find an equilibrium point for the described supply-demand situation. You may assume that the supply and demand equations are both linear.
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- 28. (a) Under what conditions do we say that two random variables X and Y are independent? (b) Demonstrate that if X and Y are independent, then it follows that E(XY) = E(X)E(Y); (e) Show by a counter example that the converse of (ii) is not necessarily true.arrow_forward7. [10 marks] Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G of length 5. We show how to find a longer cycle in G. (a) Let x be a vertex of G that is not on C. Show that there are three C-paths Po, P1, P2 that are disjoint except at the shared initial vertex and only intersect C at their final vertices. (b) Show that at least two of P0, P1, P2 have final vertices that are adjacent along C. (c) Combine two of Po, P1, P2 with C to produce a cycle in G that is longer than C.arrow_forward1. Let X and Y be random variables and suppose that A = F. Prove that Z XI(A)+YI(A) is a random variable.arrow_forward
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage