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spring2008stat201-hw05KEY

spring2008stat201-hw05KEY - 36-201 Spring 2008 Homework 5...

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This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html 36-201 Spring 2008 Homework 5 – KEY
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Stat 201 Spring 2008 Page 1 of 6 Homework 5 – KEY This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html ° Due: Wednesday, February 20 , at the beginning of lecture. Homework considered late beyond the first 10 minutes of lecture. ° Late Homework Policy: Late homework may be turned-in for a maximum of half credit, up to 4:00 PM on the same Wednesday the homework is due. Late homework should be placed in the manila envelope which will be posted by room 328-C, Facilities Management Building (FMS). Late homework should be labeled with the course as well as your name. Please do not turn in any homework to any mailboxes. ° Please include the top-page ‘coversheet’, filled-out and stapled to your homework. ° Show all work. This homework covers chapter 5 in the course textbook. Point Distribution: Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 effort & neatness TOTAL 18 10 10 36 6 20 100 NOTE: To save paper, you are encouraged to print double-side (‘duplex’ mode).
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Stat 201 Spring 2008 Page 2 of 6 Homework 5 – KEY This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html 1. Suppose a particular ‘sample space’ of elements consists of the following words, written just as shown: { A pple, B ox, cerea L , D o G , elephant } Suppose X is the event ‘beginning with a capital letter’; suppose Y is the event ‘ending with a capital letter’. 1 (a) What are the elements of X? Answer: { A pple , B ox , D o G } 1 (b) What are the elements of Y? Answer: { cerea L, D o G } 1 (c) According to the mathematical use of the word ‘and,’ what elements make up ‘X and Y’? Answer: { D o G } 1 (d) According to the mathematical use of the word ‘or,’ what elements make up ‘X or Y’? Answer: { A pple , B ox , C ereal , D o G } 2. Around town are signs that read, “Rollerblading and Skateboarding prohibited.” 2 (a) Interpreting the sign according to the strict mathematical use of ‘and’ as used in probability, am I violating the rules if I’m just rollerblading? Say yes or no ; then briefly explain your answer. Answer: No, I would not be violating the rules if I was only rollerblading. Mathematically, ‘AND’ means both together; so I would only be violating the rules if I was doing both simultaneously. 2 (b) Suppose the sign was changed to read, “Rollerblading or Skateboarding prohibited.” In that case, interpreting the sign according to the strict mathematical use of ‘or’ as used in probability, would I be violating the rules if I was on a skateboard while wearing rollerblades [assuming such a thing were physically possible]? Say yes or no ; then briefly explain your answer. Answer: Yes, I would still be violating the rules if I was doing both activities simultaneously.
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