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1) The following data are a random sample from a normal distribution of rainbow trout length and weight. For the LENGTH data: a. Calculate the MLE of the mean and variance of the distribution b. Calculate the 95% confidence interval for the mean. c. Calculate the 95% confidence interval for the variance. d. Calculate the 95% confidence interval for the standard deviation. Fish Length Weight 1 4.6 1.4904 2 4.4 1.1711 3 4.3 1.2471 4 4.3 1.0174 5 4.4 1.161 6 4.5 1.302 7 4.6 1.2409 8 4.4 1.2004 9 4.2 0.9793 10 5.1 1.9465 11 4.3 0.9406 12 4.2 1.1231 13 4.4 1.2142 14 4.6 1.3685 15 5.3 2.2767 2) Suppose X1, X2, X3, Xn is a random sample from some population, M is the median of the sample, and MAD is the median absolute deviation defined as the median of the expressions |Xi-M|, j= 12,3, , n. Show that this estimator of the variance has a breakdown value of 50%.

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