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Unformatted text preview: FRE 6083 Homework 1 Question 1 Suppose that a number u1D465 is to be selected from the real line u1D446 , and let u1D434 , u1D435 , and u1D436 be the events represented by the following subsets of u1D446 , where the notation { u1D465 : −−−−} denotes the set ocontaining every point u1D465 for which the proporty presented following the colon is satisfied: u1D434 = { u1D465 : 1 ≤ u1D465 ≤ 5 } , u1D435 = { u1D465 : 3 < u1D465 ≤ 7 } , u1D436 = { u1D465 : u1D465 ≤ } . Describe each of the following events as a set of real numbers: (a) u1D434 u1D450 (b) u1D434 ∪ u1D435 (c) u1D435u1D436 u1D450 (d) u1D434 u1D450 u1D435 u1D450 u1D436 u1D450 (e) ( u1D434 ∪ u1D435 ) u1D436 Question 2 Let u1D446 be a given sample space and let u1D434 1 ,u1D434 2 ,... be an infinite sequence of events. For u1D45B = 1 , 2 ,..., let u1D435 u1D45B = uni222A.alt01 ∞ u1D456 = u1D45B u1D434 u1D456 and let u1D436 u1D45B = uni2229.alt01 ∞ u1D456 = u1D45B u1D434 u1D456 . Show that u1D435 1 ⊃ u1D435 2...
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This note was uploaded on 02/16/2011 for the course FE 6083 taught by Professor Neveskyi during the Spring '11 term at NYU Poly.
 Spring '11
 Neveskyi

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