In this assignment, you have to construct a random interval and find a confidence interval for the population median m of the given parametric distribution f(- It?) with an unknown parameter(s) 6 by using the limiting result of the sample median discussed in lecture, i.e. .. d1 1 (X0_5 m) ) N (0, m) to answer the questions below. Note that although the form off is known, m and 9 are both unknown. So, we cannot apply the above result directly to get the intervals. *Although the limiting result is found for the sample median 305, technically speaking, any other sample median can also be shown to have the same result. Question: (3) Assume that the data come from a Gamma distribution with its pdf given by f B\" a- _, . fola)=i I\"(ax 19E ' lfx>0 0 , otherwise where 0 0 for any x > 0. Consider the following estimators ~ def (2)2 '" def X a = 2 forest, and 3 = 2 for, 5111 571-1 with the generalized continuous mapping theorem: If W\{iii} Use the random variable in (ii) and the limiting result of the sample median to construct a random interval for m. {iv} Find the 95% confidence interval for m with the data in dataset1_Ch2.txt on canvas. Remarks: dgammalt, ratez, shape=} in R can be used to find the value of the pdf of a Gamma distribution at point t by specifying the value of rate for 3 (or its estimate) and the value of shape for a [or its estimate). Other R functions that you may need to use: medianlx): sample median of the data in x. mean(x): sample mean of the data in x. varlx): sample variance of the data in x