The life time of an electronic component has exponential distribution with mean . 10 such components are put on test at the same time and the experiment is terminated as soon the second failure occurs. Based on this information on the times of rst two failures

1)Derive the level = 0.05 UMP test of H₀ : 2 against the alternative H₁ : > 2.

2) Find the null distribution of the test statistic.

3)Find an expression for the power function of this test and Plot it.