(Solved): solve number 10 in detail  10. Let the pdf of the population \( X \) be \( f(x)=e^{x-\mu} \) fo ...

10. Let the pdf of the population \( X \) be \( f(x)=e^{x-\mu} \) for \( x \leq \mu, 0 \) otherwise, with the renl parameter \( \mu \). We take a sample of size \( n=1 \). The hypothesis \( H_{0} \) says \( \mu \leq 2 \), whereas \( H_{1} \) claims \( \mu>2 \). Find a level \( \alpha=0.02 \) UMP hypothesis test. Calculate the power of the test.