# quiz1 - n th time and write it in a closed form(ie not an...

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Math 10C (Overholser) Quiz 1 Oct. 8, 2010 Name: TA: Section: 1. (5 points) Consider the distribution of height of trees in a forest where there are many short trees, few medium sized trees and many tall trees. (a) Graph a possible density function (pdf) for the distribution described above. Please label the axes of your graph. (b) Graph a possible cumulative distribution function (cdf) for the distribtion described above. Please label the axes of your graph.

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2. (5 points) A ball is dropped from a height of 15 feet and bounces. Each bounce is 2 3 of the height of the bounce before. (a) Find an expression for the total vertical distance the ball has travelled when it hits the ﬂoor for the third time. Solution: 15 + 2( 2 3 )(15) + 2( 2 3 ) 2 (15) = 145 3 (b) Find an expression for the total vertical distance the ball has travelled when it hits the ﬂoor for the
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Unformatted text preview: n th time and write it in a closed form (ie, not an inﬁnite sum). Solution: The total vertical distance travelled when the ball hits the ﬂoor for the n th time is 15 + 2( 2 3 )(15) + 2( 2 3 ) 2 (15) + 2( 2 3 ) 3 (15) + · · · + 2( 2 3 ) ( n-1) (15) . Notice that 15 + ( 2 3 )(15) + ( 2 3 ) 2 (15) + ( 2 3 ) 3 (15) + · · · + ( 2 3 ) ( n-1) (15) is a ﬁnite geometric series with n terms, a = 15 and x = 2 3 and so sums to 15(1-( 2 3 ) n ) 1-2 3 = 45(1-( 2 3 ) n ) . The total distance can then be expressed in closed form as 2 ± 45(1-( 2 3 ) n ) ²-15 = 90 ± (1-( 2 3 ) n ) ²-15 . Page 2...
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## This note was uploaded on 11/07/2010 for the course MATH 10C math 10c taught by Professor Rosanna during the Spring '10 term at UCSD.

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quiz1 - n th time and write it in a closed form(ie not an...

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