Answer Happy

4. [11 marks] Suppose that levels of background radiation in a city are given by the following pdf, with parameter : f(y; 2) = ye-8y2/2 A random sample of n independent background radiation measurements, 71, 72, ... Yn , is to be collected in a city. a. [3] Based on a random sample of n observations, show that the MLE for 0 is Ô =; 2n Show all work. מין 21=YT b. [3] Based on a random sample of n observations, now derive an expression for r(@). You can use the mle in part a. even if you weren't able to answer that part. c. [5] Based on a random sample of n = 60 background radiation measurements taken in a city, it was determined that if y} = 120. Use this summary information, your results from parts a. and b. of this question to test Ho: 0 = 0.9 by conducting a likelihood ratio test. Calculate the approximate p-value and use the guidelines from page 128 of the Course Notes to assess the amount of evidence against H., based on the data. Be sure to show all steps clearly and show all relevant work in your solution (as noted in question 1).