The lifetime in hours of each bulb manufactured by a particular company follows an independent exponential distribution with mean λ. To test the null hypothesis H0 : λ = 1000 against the alternative H1 : λ = 500, a statistician sets up an experiment with 50 bulbs, with 5 bulbs in each of 10 ddifferent locations, to examine their lifetimes. To get quick preliminary results, the statistician decides to stop the experiment as soon as one bulb fails at each location. Let Yi denote the lifetime of the first bulb to fail at location i. Obtain the most powerful test of H0 against H1 based on Y1, Y2, . . . , Y10, and compute its power.