spring2008stat201-hw06KEY

spring2008stat201-hw06KEY - 36-201 Spring 2008 Homework 6...

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This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html 36-201 Spring 2008 Homework 6 – KEY
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Stat 201 Spring 2008 Page 1 of 7 Homework 6 – KEY This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html ° Due: Wednesday, February 27 , 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 parts of chapter 6 in the course textbook. For grading purposes: Exercise 1 Exercise 2 Exercise 3 Exercise 4 effort & neatness TOTAL 19 13 8 40 20 100 NOTE: To save paper, you are encouraged to print double-sided (‘duplex’ mode). 1. The U.S. Census Bureau compiles data that describe many features of the population. One of the questions they ask to women of child-bearing age is, “How many children have you had?” Based on results published for 2004, the probability distribution of the number of children, X, that a randomly-selected U.S. woman of child-bearing age will have had is represented by the following table:*
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Stat 201 Spring 2008 Page 2 of 7 Homework 6 – KEY This document available on: http://www.stat.cmu.edu/~gordonw/spring2008stat201.html X 0 1 2 3 4 5 or more P(X) . 45 . 17 . 22 . 11 . 04 . 01 * Available online: http://www.census.gov/population/socdemo/fertility/cps2004/tab01-01.xls (Probabilities have been rounded to the nearest percent for simplicity.) 1 (a) How many variables are represented in the distribution? Is (or are) the variable(s) discrete or continuous ? Answers: There is one variable (number of children). It is discrete (since number of children can only be the ‘separated’ values 0, 1, 2, etc.) 1 (b) Verify that this is a legitimate probability distribution. (Give brief explanation or show any calculation you perform.) Solution: Each probability is obviously between 0 and 1 (i.e., non-negative and not greater than 1); and the probabilities sum to 1: .45 + .17 + .22 + .11 + .04 + .01 = 1 1 (c) Say in words what “P(X 3)” represents in terms of the actual scenario; then compute P(X 3). [show work.] Solution: “P(X 3)” represents the probability that a (randomly selected) woman will NOT have 3 children.
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