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.