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. (Or equivalently, the proportion of women in the population
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This note was uploaded on 02/01/2009 for the course STAT 36-201 taught by Professor Gordon during the Fall '08 term at Carnegie Mellon.

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

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