The exponential distribution is f (x; ) = ex and E(X) = 1.

Chapter , Problem 30

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The exponential distribution is \(f(x ; \lambda)=\lambda e^{-\lambda x}\) and \(E(X)=\lambda^{-1}\). The cumulative distribution function is \(F(x)=P(X \leq x)=1-e^{-\lambda x}\). Three observations are made by an instrument that reports \(x_{1}=5\) and \(x_{2}=3\), but \(x_3\) is too large for the instrument to measure and it reports only that \(x_{3}>10\). (The largest value the instrument can measure is 10.0.)

a. What is the likelihood function?

b. What is the mle of \(\lambda\)?

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