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hw3_solns

# hw3_solns - ORIE 4580 5580 5581 Solutions for Homework...

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ORIE 4580 / 5580 / 5581 Solutions for Homework Assignment 3 Question 1 a) Fraction of the points that fall under the curve = Area under the curve / Area of the square = . 4 / ) 0 1 ( ) 0 1 ( 1 1 0 2 du u b) The following sheet computes the number of points required in cell G10. A B C D E F G 1 rep. x y inside region? 2 1 =RAND() =RAND() =IF(C2<SQRT(1-B2^2),1,0) average =AVERAGE(D2:D51) 3 =A2+1 =RAND() =RAND() =IF(C3<SQRT(1-B3^2),1,0) std. dev. =STDEV(D2:D51) 4 =A3+1 =RAND() =RAND() =IF(C4<SQRT(1-B4^2),1,0) 5 =A4+1 =RAND() =RAND() =IF(C5<SQRT(1-B5^2),1,0) desired half width 0.01 6 =A5+1 =RAND() =RAND() =IF(C6<SQRT(1-B6^2),1,0) conf. level 0.9 7 =A6+1 =RAND() =RAND() =IF(C7<SQRT(1-B7^2),1,0) alpha =1-G6 8 =A7+1 =RAND() =RAND() =IF(C8<SQRT(1-B8^2),1,0) z =-NORMINV(G7/2,0,1) 9 =A8+1 =RAND() =RAND() =IF(C9<SQRT(1-B9^2),1,0) 10 =A9+1 =RAND() =RAND() =IF(C10<SQRT(1-B10^2),1,0) N =ROUNDUP(((G8*G3)/G5)^2,0) 11 =A10+1 =RAND() =RAND() =IF(C11<SQRT(1-B11^2),1,0) This spreadsheet uses the formula 2 2 / ~ l s z N k , where l is in G5, k s ~ is in G3 and 2 / z is in G8.

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hw3_solns - ORIE 4580 5580 5581 Solutions for Homework...

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