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HW1 - Math 126 Name section HW#1 PID Sep 17 2008...

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Math 126 section HW #1 Sep. 17, 2008 Name: PID: INSTRUCTIONS : Solve the following problems and show your work in the place provided. You must show your work! Points may be withdrawn for the answers given without substantiation! Place your answers in the underlines, where provided. 1. The graph of the derivative function F 0 ( x ) of F ( x ) is given by the graph below. - 6 x y -1 1 2 3 4 5 6 7 8 -2 2 4 6 F 0 ( x ) (a) (1 Point) What is the value of F 0 (0)? (b) (1 Point) True or False: F ( x ) has a local maximum at x = 5. (c) (1 Point) Find the value of Z 8 0 F 0 ( x ) dx . 1

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(d) (1 Point) Find the value of F (8) - F (0). (e) (1 Point) Suppose that F (0) = - 4. Then find the value of F (8). 2. p ( x ) is a density function in the following graph: - 6 x y | | . . . . . . . . . . . . . . . . . . . . . -1 1 c o (a) (1 point) Find the value c . (b) (1 point) Find the horizontal line equation of p ( x ). (c) (1 point) Find the cumulative distribution function P ( t ). 2
3. The density function p ( t ) of the waiting time t (in minutes) at a busy trafic intersection is modeled as follows: p ( t ) = ( 0 if t < 0 0 . 6 e - 0 . 6 t if t 0 (a) (1 point) Find the formula for the cumulative distribution function P ( x ). (b) (1 point) Find the percentage of people who have to wait less than 1 minute at the

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