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Two experiments, Experiment 1 and Experiment 2, measure the same quantity Y 20 times. The measurements result in the numbers: Experiment 1: Y¹ = [ 34.3, 41.1, 37.2, 47.3, 34.8, 42.7, 39.8, 41.4, 35.9, 41.4, 38.9, 42.8, 40.9, 38.5, 43.4, 36.1, 44.4, 33.1, 38.2, 37.3] Experiment 2: Y² = [ 42.2, 43.3, 36.6, 43.1, 36.5, 47.8, 46.9, 48.8, 35.8, 44.3, 36.2, 55.8, 45.5, 35.6, 46.2, 36.6, 42.7, 37.3, 32.7, 43.4] There is some reason to belief that the two experiments are not uncorrelated. a) Calculate the means and the (unbiased) standard deviations for each experiment in an unbiased way. b) Calculate the (unbiased) covariance and the Pearson correlation coefficient between the two experiments. Write down the covariance matrix. c) Calculate the uncertainty on the means of each measurement. d) Calculate the weighted average of the means of the two measurements. e) Calculate the covariance of the means of the two experiments, using the above calculated value of the correlation. Check the compatibility of the two measurements, taking into account the correlation.

Two experiments, Experiment 1 and Experiment 2, measure the same quantity Y 20 times. The measurements result in the numbers: Experiment 1: Y¹ = [ 34.3, 41.1, 37.2, 47.3, 34.8, 42.7, 39.8, 41.4, 35.9, 41.4, 38.9, 42.8, 40.9, 38.5, 43.4, 36.1, 44.4, 33.1, 38.2, 37.3] Experiment 2: Y² = [ 42.2, 43.3, 36.6, 43.1, 36.5, 47.8, 46.9, 48.8, 35.8, 44.3, 36.2, 55.8, 45.5, 35.6, 46.2, 36.6, 42.7, 37.3, 32.7, 43.4] There is some reason to belief that the two experiments are not uncorrelated. a) Calculate the means and the (unbiased) standard deviations for each experiment in an unbiased way. b) Calculate the (unbiased) covariance and the Pearson correlation coefficient between the two experiments. Write down the covariance matrix. c) Calculate the uncertainty on the means of each measurement. d) Calculate the weighted average of the means of the two measurements. e) Calculate the covariance of the means of the two experiments, using the above calculated value of the correlation. Check the compatibility of the two measurements, taking into account the correlation.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Two experiments, Experiment 1 and Experiment 2, measure the same quantity Y 20 times. The measurements result in the numbers: Experiment 1: Y¹ = [ 34.3, 41.1, 37.2, 47.3, 34.8, 42.7, 39.8, 41.4, 35.9, 41.4, 38.9, 42.8, 40.9, 38.5, 43.4, 36.1, 44.4, 33.1, 38.2, 37.3] Experiment 2: Y2 = [ 42.2, 43.3, 36.6, 43.1, 36.5, 47.8, 46.9, 48.8, 35.8, 44.3, 36.2, 55.8, 45.5, 35.6, 46.2, 36.6, 42.7, 37.3, 32.7, 43.4] There is some reason to belief that the two experiments are not uncorrelated. a) Calculate the means and the (unbiased) standard deviations for each experiment in an unbiased way. b) Calculate the (unbiased) covariance and the Pearson correlation coefficient between the two experiments. Write down the covariance matrix. c) Calculate the uncertainty on the means of each measurement. d) Calculate the weighted average of the means of the two measurements. e) Calculate the covariance of the means of the two experiments, using the above calculated value of the correlation. Check the compatibility of the two measurements, taking into account the correlation.
Transcribed Image Text:Two experiments, Experiment 1 and Experiment 2, measure the same quantity Y 20 times. The measurements result in the numbers: Experiment 1: Y¹ = [ 34.3, 41.1, 37.2, 47.3, 34.8, 42.7, 39.8, 41.4, 35.9, 41.4, 38.9, 42.8, 40.9, 38.5, 43.4, 36.1, 44.4, 33.1, 38.2, 37.3] Experiment 2: Y2 = [ 42.2, 43.3, 36.6, 43.1, 36.5, 47.8, 46.9, 48.8, 35.8, 44.3, 36.2, 55.8, 45.5, 35.6, 46.2, 36.6, 42.7, 37.3, 32.7, 43.4] There is some reason to belief that the two experiments are not uncorrelated. a) Calculate the means and the (unbiased) standard deviations for each experiment in an unbiased way. b) Calculate the (unbiased) covariance and the Pearson correlation coefficient between the two experiments. Write down the covariance matrix. c) Calculate the uncertainty on the means of each measurement. d) Calculate the weighted average of the means of the two measurements. e) Calculate the covariance of the means of the two experiments, using the above calculated value of the correlation. Check the compatibility of the two measurements, taking into account the correlation.
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