15. From a sample of items having an exponential life distribution with unknown mean , items are...

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15. From a sample of items having an exponential life distribution with unknown mean θ, items are tested in sequence. The testing continues until either the rth failure occurs or after a time T elapses.

(a) Determine the likelihood function.

(b) Verify that the maximum likelihood estimator of θ is equal to the total time on test of all items divided by the number of observed failures.

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Somshukla Chakraborty

I have a teaching experience of more than 4 years by now in diverse subjects like History,Geography,Political Science,Sociology,Business Enterprise,Economics,Environmental Management etc.I teach students from classes 9-12 and undergraduate students.I boards I handle are IB,IGCSE, state boards,ICSE, CBSE.I am passionate about teaching.Full satisfaction of the students is my main goal. I have completed my graduation and master's in history from Jadavpur University Kolkata,India in 2012 and I have completed my B.Ed from the same University in 2013. I have taught in a reputed school of Kolkata (subjects-History,Geography,Civics,Political Science) from 2014-2016.I worked as a guest lecturer of history in a college of Kolkata for 2 years teaching students of 1st ,2nd and 3rd year. I taught Ancient and Modern Indian history there.I have taught in another school in Mohali,Punjab teaching students from classes 9-12.Presently I am working as an online tutor with concept tutors,Bangalore,India(Carve Niche Pvt.Ltd.) for the last 1year and also have been appointed as an online history tutor by Course Hero(California,U.S) and Vidyalai.com(Chennai,India).

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