maple_test1 - iii 0ÐBÑ-2 Suppose a random variable has a...

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Maple Take Home Test 1 Math 41L Fall 11 name __________________________ Use to answer the questions below. You may also use the text, Maple tutorial or your Maple class notes, but you should not talk to any one other than the instructor about these questions until after the assignment is due. Attach to this cover sheet, a worksheet in which you solve the problems below and Maple explain your reasoning so that someone who hasn't read the problem can follow your reasoning. Make sure your name is on any additional paper you hand in. 1. Consider the function ln on the interval Find the value of which 0ÐBÑ o B B  B Ò"ß %ÓÞ - satisfies the mean value theorem for on the interval Then, plot together the following 0ÐBÑ Ò"ß %ÓÞ three graphs: ( ) ; i 0ÐBÑ ( ) the line connecting the endpoints and ; and ii Ð"ß 0Ð"ÑÑ Ð%ß 0Ð%ÑÑ ( ) the tangent line to at .
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Unformatted text preview: iii 0ÐBÑ-2. Suppose a random variable has a probability density function (i.e. probability mass \ function) given by for :Ð\ o 3Ñ o 3 o "ß #ß $ß â&!Þ-3 (a) What is the constant ?-(b) What is the probability that to two decimal places? \ #& (c) What is the expected value of to two decimal places? \ 3. (a) Use Maple to find the volume of the solid of revolution found by revolving the region bounded by sin , , and about the -axis. Give the 0ÐBÑ o ÐB Ñ B o ! C o ! B o " B # answer to three decimal places. (b) Use Maple to compute a right hand sum with n = 200 subintervals which approximates the quantity computed in (a). Give the error of this approximation to three decimal places. I have adhered to the Duke Community Standard in completing this assignment. :___________________________________ Signature...
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