Let X1, . . . , Xn be an i.i.d. sample from a distribution with density function

Let X1, ..., Xn be an i.i.d. sample from a distribution with density function 1 f(x|0) = 20 exp n and let T = CIXil. i=1 1. Show that 27/o has a chi-square distribution and find its degrees of freedom. Hint: What is the distribution of |X1|? Now, let n = 100. Consider the test that rejects Ho : o = 10 in favor of H1 : o * 10 for [T - 1000) > 200. 2. What is a? 3. Graph the power as a function of o for 1