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Unformatted text preview: Lecture 3 ReCasting Classic Textbook Problems in Terms of Random Variables Example 1 (2.36) An electronics firm plans to build a new research laboratory in Southern California, and its management has to decide between sites in Los Angeles (LA), San Diego (SD), Long Beach (LB), Pasadena (Pa), Santa Barbara (SB), Anaheim (An), Santa Monica (SM), and Westwood (We). If A represents the event that they will choose SD or SB, B represents the event that they will choose SD or LB, C represents the event that they will choose SB or An, and D represents the event that they will choose LA or SB, list the elements of each of the following subsets of the sample space which consists of the eight site selections: (a) A’ : ______________________________________________________ (b) D’ :______________________________________________________ (c) D C ∩ : ___________________________________________________ Solution without Random Variables : Step #1: Read the entire statement. Then identify the overall setting A decision must be made to choose one of 8 possible sites for the facility. The collection of possible sites is { LA, SD, LB, Pa, SB, An, SM, We }= Ω. Step # 2: Summarize given details in concise terms A = {SD, SB} ; B = {SD, LB} ; C = {SB, An} ; D = {LA, SB} Step #3: Make sure you understand the mathematical notation A’ is everything in Ω except for that which is in A. [i.e. the complement of A ] D’ is everything in Ω except for that which is in D. [i.e. the complement of D ] D C ∩ is everything that is common to C and D [i.e. their intersection ] Now the answers ‘should be easy’. Fill in the answers above. ReCasting the Problem in Terms of Random Variables : Step #1: Read the entire statement. Then identify the overall setting A decision must be made to choose one of 8 possible sites for the facility. Let the act of recording a decision be denoted as X . The collection of possible sites is { LA, SD, LB, Pa, SB, An, SM, We }= Ω. Identify this set with the set of numbers { 1, 2, 3, 4, 5, 6, 7, 8} = S X . This set is the sample space for X. Step # 2: Summarize given details A = {2, 5} ; B = {2, 3} ; C = {5, 7} ; D = {1, 5} Step #3: Make sure you understand the mathematical notation A’ is everything in Ω except for that which is in A. [i.e. the complement of A ] D’ is everything in Ω except for that which is in...
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 Spring '09
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