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# CALCULUS II MATH 142

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This 3 page Class Notes was uploaded by Cassidy Grimes on Monday October 26, 2015. The Class Notes belongs to MATH 142 at University of South Carolina - Columbia taught by D. Meade in Fall. Since its upload, it has received 28 views. For similar materials see /class/229533/math-142-university-of-south-carolina-columbia in Mathematics (M) at University of South Carolina - Columbia.

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Date Created: 10/26/15

Math 142 Lab Project 3 Due Fri March 26 by 500 PM Assignment Your third lab project consists of the three questions from the back of this page Each question is worth 10 points Collaboration You may work with others but each student should submit a separately written project report At the end of your report you should list all of your collaborators Simply copying another s work and calling it your own or not giving credit to collaborators is considered plagiarism and will be dealt with according to University regulations What makes a good report Your nal report for each project should have a clear and complete presentation of the project material Each report will generally consist of paragraphs of text interspersed between various Maple commands plots and other output All text should be written with complete sentences using proper grammar and correct spelling A part of your grade will be based upon the clarity of your presentation When proofreading your report check to see if you are omitting important details or illustrative plots Also check to see if you are including too many unnecessary details Hand in work that you are proud to claim as your own In particular do not simply turn in a Maple worksheet with a bunch of input and output It is not the TA s job to gure out how your Maple output answers the various questions It is your job to submit an easytoread project report You may use pencil and paper Microsoft Word with bits of output copied from Maple Maple with text regions or any other format which allows you to submit a clearly written report Note also that you are not required to use Maple for all parts of your project Some work is more easily done by hand Submit proiect reports to your Lab TA due Fri March 26 by 500 PM Sections 1 7 3 with Prof Dix Lab TA Qi Wu Contact Info wugmathscedu LC 107B 5765948 mailbox for Wu Qi by LC 411 Sections 4 7 6 with Mr Murphy Lab TA Elizabeth Perez Contact Info perezemathscedu LC107B 5765948 mailbox for Perez by LC 411 Sections 7 7 9 with Prof Bennett Lab TA Luke Owens Contact Info owens1mathscedu LC B004 7774674 mailbox for Owens L by LC 411 Probability De nitions and Terminology o A random uariable is a quantity that can be measured or determined but might vary each time the experiment is repeated For example if the experiment is ipping a coin until a head appears the number of ips before seeing a head is a discrete random variable The number of hours that a lightbulb burns before failing is an example of a continuous random variable A probability density function or pdf for a continuous random variable X is a function 1 de ned on foo 00 with the properties 1 x 2 0 for all foo lt z lt oo lt2 fe 1251 o The probability that X takes on a value between a and b is b Pr0ba X g b dm 0 The mean or expected value of a continous random variable X with pdf 1 is de ned to be 00 M ElX mm dz 00 provided this improper integral exists 0 The uariance of X is de ned to be 00 a Varle EX e m z 7 WM dm 00 provided this improper integral exists NOTE 0 is called the standard deuiation of X o The median value of X is de ned to be the number m such that 135 135 o The cumulatiue distribution function or cdf for X is the function F with the property that 12 Fz ProbX z ft dt 00 where f is the pdf for X MAPLE LAB FOR CALCULUS 11 Spring 2004 Problems 1 Which of the following are probability density functions Explain 1 a 7 7m713x77 1f0 m 3 ltagtfltwgtes meow 4m72z2 if0 m 2 bf 0 ifmlt00rmgt2 C 2 Determine the value of C which will make fz 2 a probability density function Using this value of C7 obtain a formula for the cumulative distribution function which corresponds to this pdf Now sketch graphs of fz and together on the same set of axes 3 The probability density function for the number of miles that a car can run before its newly installed battery wears out is 015411m iszO 09 0 in lt 0 where z is measured in thousands of miles a Sketch the graph of this probability density function b What is the probability that a newly installed battery will wear out at some point between the car being driven 1000 miles and 3000 miles c Suppose you ve just installed a new battery in your car and would like to take a 5000 mile trip What is the probability that you will be able to complete your trip before your car battery wears out d What is the mean number of miles that a newly installed car battery will last before wearing out e What is the median number of miles that a newly installed car battery will last before wearing out Explain the geometric signi cance of this value in terms of areas under the graph of f If the probability that a newly installed battery wears out in less than T miles is 0757 then what is the value of T MAPLE LAB FOR CALCULUS H 2 Probability

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