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# Sp01ex2 - 8.4545 Sp 01 EGN 3420 EXAM 2 Name Show All Work...

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Sp 01 EGN 3420 EXAM 2 Name __________________ Show All Work! Problem 1 (35 pts) The data points ( , ) x y i i in the table below are to be approximated by a second order polynomial y a a x a x = + + 0 1 2 2 . x i y i y i e y y i i i = - e i 2 -1 -1 0 0 1 1 2 8 3 27 a) Find the Normal Equations which are used to solve for the least squares coefficients a a a 0 1 2 , , . b) Solve the Normal Equations to find the Least Squares quadratic through the data points. c) Fill in the table and find the SST, SSE, SSR and the correlation coefficient r .

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Sp 01 EGN 3420 EXAM 2 Name __________________ Show All Work! Problem 2 (35 pts) Fit a saturation growth rate equation to the data representing population (in millions) of a city i P at a time i t years after some reference date. (years) i t 6 (10 people) i P
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Unformatted text preview: 8.3333 10 33.3333 25 41.6667 50 45.4545 Sp 01 EGN 3420 EXAM 2 Name __________________ Show All Work! Problem 3 (30 pts) The probability that a Normally distributed random variable X with mean 0 and standard deviation 1 falls within the range 1 to x x is given by the integral of the probability density function ( ) f x form x to 1 x . In other words, 1 1 ) ( ) Pr( x x f x dx x X x < < = ∫ where ( ) f x is given by 2 1 ( ) exp( ) 2 2 x f x π =-Estimate 2) Pr( X < < using Trapezoidal Integration with 10 intervals. i x i f i = f ( x i ) 0.0000 1 2 3 4 5 6 7 8 9 10 2.0000 Round all calculations to 4 places after the decimal point....
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