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Are the following statements true or false (a) The

Probability and Statistics for Engineers and Scientists | 4th Edition | ISBN: 9781111827045 | Authors: Anthony J. Hayter ISBN: 9781111827045 235

Solution for problem 2.9.19 Chapter 2

Probability and Statistics for Engineers and Scientists | 4th Edition

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Probability and Statistics for Engineers and Scientists | 4th Edition | ISBN: 9781111827045 | Authors: Anthony J. Hayter

Probability and Statistics for Engineers and Scientists | 4th Edition

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Problem 2.9.19

Are the following statements true or false? (a) The variance of a random variable is measured in the same units as the random variable. (b) In a diving competition, the scores awarded by judges for a particular type of dive have an expected value of 78 with a standard deviation of 5. If the scores are doubled so that they can be compared with scores fromaneasiertypeofdive,thenewscoreswillhavean expected value of 156 and a standard deviation of 10. (c) The variance of the difference between two independent random variables cannot be smaller than the larger of their two variances. (d) If a continuous random variable has a symmetric probability density function, then the mean and the median are identical. (e) If X is a continuous random variable, then P(X x) = P(X > x) for any value of x. (f) If X is a discrete random variable, then P(X x) = P(X > x) for any value of x.

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Jenny Lundberg CI427—Mohr April 9, 2016 Class Notes Agenda 1. Cookbook vs Inquiry revisited 3. FACTs Presentation 3. Workshop 4. Collaboration 5. Check In/Up Time Cookbook vs Inquiry revisited Article: Inquiry On Board (October 2006)  My personal Notes: o Brainstorm  As a class, discuss possible variables that can be seen in a specific experiment. o Choose Variable  Manipulated variable (independent variable)  Responding variable (dependent variable)  Controlled variables o Ask a Question  Question is tied to the manipulated variable o Predict and Outcome  Teacher models how to form a prediction  Students need to justify their thinking o Set up Experiment  Use an inquiry board to organize and sequence how they would like to organize the experiment.  Limit students to one experiment of inquiry.  Use diagrams in journals to keep them understanding and tracking their experiment. o Table of Results  Record observations.  Create data table.  The effect of the manipulated variable isn’t known yet. o Look for Patterns and Graph of Results  Present information on a graph.  The visual will help students to answer their question. o Answer the Question  The answer is found between the data and the graph  Class discussion: o Reviews the scientific method and how you might use it in the classroom. o Used manipulated and responding variables instead of independent and dependent variables. o The students are able to determine their own variables (open inquiry) instead of given the set of variables they must use (cookbook inquiry) o There is an importance of having multiple tests and tracking data. o Helps the students focus on variables instead of an experiment itself. The Four Question Research Strategy by Cothron, Giese and Rezba. Students and Research. 2000 Activity: The Grandfather’s Clock—Setting up Experiment  Notes from the story o In the grandfather clock, you use the pendulum of the clock to keep the clock telling time by it swinging back and forth; tick­tock. o Then a key is used once a week to wind and keep the pendulum going. o In the story, two weeks pass and the characters observe that the grandfather clock moves slower than a regular clock. o The character wants the clock to go faster! Character thinks:  Maybe I need to swing the pendulum faster  Maybe I need to give the pendulum less weight  Maybe I need to shorten the length of the pendulum  Setting up experiment, finding different variables to test: o Manipulating the mass (my group) o Manipulating the angle of the swing o Manipulating the string length Activity: The Crooked Swing—Make a Model  Notes from the story o Problem is that the swing is crooked. o Variable: changing length of chains. Results: Same results. o Characters create a model and find out what made it go crooked.  Setting up our models o Tie stings together and open into a T­formation. o Answers was that the strings had to be made the same length. (Although, the swing was now tilted and not parallel to the ground) Cookbook Lab: Investigating Pendulums  Lab write up from Flinn.  It gives the process and variables.  Students would just follow directions and not make any natural inquiry to the process. FACTs Presentation Topic: Juicy Questions  Stretch the students thinking so they look deeper for information to find an answer to a questions.  It is usually a BIG question that will bring about smaller questions to guide students into finding the answer.  Supports students learning.  There is not necessarily just one right answer because students will access different parts of their schema when getting towards the answers.  The teacher just needs to scaffold so that they students are going in the right direction of thought.  Whole group collaboration bring a collection of knowledge and is beneficial for other students to hear one another’s thoughts.  Example: “How does the water cycle work” A student may start asking questions about particular steps in the process to get the whole answer.  We try it!: If a bowling ball and feather are dropped at the same time in a vacuum, what will hit the ground first  YouTube Video: Brian Cox visits the world’s biggest vacuum chamber—Human Universe: Episode 4 Preview BBC Two  If a student struggles, a teacher can prewrite a list of topics the students may need to consider before finding the way to the big question. Watching moon video of hammer and feather being dropped at the same time.  The hammer and feather land at the same time! How do we explain gravity video.  Clipped spandex represents matter in space and time.  It shows how two objects being placed on the spandex will move closer and then next to one another when both placed on the spandex.  The more mass there is, the bigger the pull is and the stronger the attraction is when new mass is added to the spandex.  They show how things orbit by giving it a motion; it is discussed that in a vacuum, the orbit would have continued in a perpetual motion. Workshop Collaboration Time Splitting up responsibilities of what is left for the project. Check In/Up Times Upcoming Due Assignments  Workshop due April 13 th  Workshop practice/run through on April 16th Flinn Science Catalog Reference Manual 2013  All teachers in IL can get one for free.  1­800­452­1261  www.flinnsci.com  This gives teachers the knowledge of possible hazards and ways to make the environment safe. Safety Data Sheets  Found on the Flinn Scientific, Inc. Website o Go to teacheh resources o Click on “sign up for a free first­year teacher’s survival kit” o Do middle school laboratory safety course  Has a PDF that tells the 3 main duties: 1. The duty to instruct and warn. 2. The duty to supervise. 3. The duty to provide a safe learning environment.  Labsafety.flinnsci.com/……… search in on Google.  Poison Control number: 1­800­222­1222 Material Safety Data Sheets (MSDS)

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Chapter 2, Problem 2.9.19 is Solved
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Textbook: Probability and Statistics for Engineers and Scientists
Edition: 4
Author: Anthony J. Hayter
ISBN: 9781111827045

This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and Scientists, edition: 4. The answer to “Are the following statements true or false? (a) The variance of a random variable is measured in the same units as the random variable. (b) In a diving competition, the scores awarded by judges for a particular type of dive have an expected value of 78 with a standard deviation of 5. If the scores are doubled so that they can be compared with scores fromaneasiertypeofdive,thenewscoreswillhavean expected value of 156 and a standard deviation of 10. (c) The variance of the difference between two independent random variables cannot be smaller than the larger of their two variances. (d) If a continuous random variable has a symmetric probability density function, then the mean and the median are identical. (e) If X is a continuous random variable, then P(X x) = P(X > x) for any value of x. (f) If X is a discrete random variable, then P(X x) = P(X > x) for any value of x.” is broken down into a number of easy to follow steps, and 157 words. The full step-by-step solution to problem: 2.9.19 from chapter: 2 was answered by , our top Statistics solution expert on 01/12/18, 03:07PM. Since the solution to 2.9.19 from 2 chapter was answered, more than 246 students have viewed the full step-by-step answer. Probability and Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9781111827045. This full solution covers the following key subjects: . This expansive textbook survival guide covers 17 chapters, and 1475 solutions.

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