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hw3(1) - ORIE 4580/5580/5581 Homework Assignment 3 Due by...

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ORIE 4580/5580/5581 Homework Assignment 3 Due by Sep. 23, 11:00 am, in the drop-box located on the second floor of Rhodes Hall. Please show your work and clearly mark your answers. Make sure that your spreadsheet printouts are properly formatted and labeled. There is no need to print out the entire sheet. The first page suffices, as long as the confidence interval calculations are shown. Hand in a printout of the formulas on your spreadsheets as well. In Excel, CTRL‘ key combination can be used to display the formulas ( key is located at the top left corner of the keyboard). Do not forget to indicate a recitation session on your homework. This is the session during which you can collect your graded work. 1. a) Assume that we generate N points { ( X n , Y n ) : n = 1 , . . . , N } uniformly distributed over the square [0 , 1] × [0 , 1]. This is the square that ranges from 0 to 1 on the x -axis and also from 0 to 1 on the y -axis. On the average, what fraction of the points would fall under the curve f ( x ) = 1 x 2 ? (Hint: The set of points ( x, y ) ∈ ℜ 2 that satisfy x 2 + y 2 = 1 form a circle with radius 1 and centered at point (0
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