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6. This question is a simple exercise in changing variables. A gun fires at random in the angular range −π/2 < 0 < π/2 towards a wall a distance away. If y is the coordinate along the wall, show that 1 g(y)dy = 1 dy π 1 + (y/l)² 1 This, as we saw in the lectures, is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L (not the same as 1) either side of the peak. Calculate the new normalisation constant, and find the standard deviation.

6. This question is a simple exercise in changing variables. A gun fires at random in the angular range −π/2 < 0 < π/2 towards a wall a distance away. If y is the coordinate along the wall, show that 1 g(y)dy = 1 dy π 1 + (y/l)² 1 This, as we saw in the lectures, is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L (not the same as 1) either side of the peak. Calculate the new normalisation constant, and find the standard deviation.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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6. This question is a simple exercise in changing variables. A gun fires at random in the angular range −π/2 < 0 < π/2 towards a wall a distance away. If y is the coordinate along the wall, show that 1 g(y)dy = 1 dy π 1 + (y/l)² 1 This, as we saw in the lectures, is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L (not the same as 1) either side of the peak. Calculate the new normalisation constant, and find the standard deviation.
Transcribed Image Text:6. This question is a simple exercise in changing variables. A gun fires at random in the angular range −π/2 < 0 < π/2 towards a wall a distance away. If y is the coordinate along the wall, show that 1 g(y)dy = 1 dy π 1 + (y/l)² 1 This, as we saw in the lectures, is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L (not the same as 1) either side of the peak. Calculate the new normalisation constant, and find the standard deviation.
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