A researcher plans to use a random sample X1, ..., Xn of size n from a population with probability density function where parameter 0 > 0. e (x|0) = { /20 f -x/20 x 0 elsewhere, 0 (a) Derive the maximum likelihood estimator for parameter 0. (b) Derive an expression for the test statistic LRS = -2ln A, where A is the likelihood ratio statistic, for undertaking a likelihood ratio test of the null hypothesis Ho: 01 against the alternative hypothesis H: 01. = (c) The researcher is concerned that the application is for a small sample size, n, and does not wish to rely on asymptotic results concerning the distribution of LRS. Explain, in detail, how you would use Bootstrap simulation methods to determine the small sample distribution of the test statistic LRS and how it could be used to undertake the above hypothesis test in small samples. You can use either the p-value or the critical region.