f(x;)=2xex/x>0. Observe that E[X]=2, so 2 represents the population average song duration. (a) Find the MLE of 2 (hint: recall the invariance principle). (b) Find the distribution of T=X/ and use it to construct exact confidence intervals for 2. (Hint: use n1i=1nXi/ as a pivotal quantity). (c) Find the asymptotic distribution of the MLE of , and use it to construct asymptotic confidence intervals for 2..