Homework 1 January 10, 2017 Please staple your homework pages in the upper left corner. [50-70 pts] Due: (a) in class Tuesday January 17 (b) in mailbox of TA Daniel Cross by close of business 1/17 1. 6.3 [ 5 pts] 2. 6.6 [ 5 pts] 3. 6.9 (a-e) [25 pts] 4. For the linear model [15 pts] Y_i = beta1 + beta2 * x_i + eps_i i=1,...,n eps_i ~ N(0,sigma^2) i.i.d. Show ( sum y_i, sum y_i^2, sum x_i * y_i ) sufficient for theta = ( beta1, beta2, sigma^2 ). Note: The values x_i are not random, but chosen by the experimenter. 5. [20 pts] [Required for 519 students; extra credit 419 students] In Tukey's Exploratory Data Analysis book, Tukey demonstrates the box-and-whiskers plot on Lord Rayleigh's data measuring the weight of nitrogen gas obtained by various means. Discrepancies in the results led to his discovery of element argon. Rayleigh made 24 measurements from 1892-1894, with mean of 2.30584 and standard deviation of 0.00537. It is common to assume such measurements of a fundamental quantity are normally distributed. Plot a contour plot of the log-likelihood and the L2E criteria as a function of the mean and the log10( standard-deviation ) over intervals ( 2.296, 2.314 ) and log10( 0.0001, 0.01 ), respectively. Note the location of the sample mean and standard deviation on each. Compare and comment on your findings. Hints: (1) In R, use x = read.csv( "rayleigh.csv", header=T ) (2) Picking contour levels to display a bit tricky, given the very large range of function values. Try several.