3. A harpsichord in a Philharmonic orchestra is being instantly replaced as soon it breaks. The harpsichord factory claims that it has been producing instruments for centuries and that each instrument has an independent lifetime given by the distribution 3Adt (1 + )+ where f parametrists time in years and 1 > 0 is a frequency parameter in years", not specified by the factory. (i) Records show that the harpsichord has been changed 10 times within 500 years. Can you estimate the parameter ? Justify your answer using independence of lifetimes. [10 mark (ii) Given that the current harpsichord has already 100 years, is it worth considering replacing it? Argue comparing the remaining lifetime cumulative distribution with the one of a brand [12 marks new one. Also compute and compare the expectation of these two lifetime distributions. (iii) Independently, a new musician joins at a random time the orchestra and decide to stay