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The two-parameter exponential. The cumulative distribution of the two-parameter exponential distribution can be written as

where µ is a location parameter and u is a scale parameter. Derive the best linear estimates of σ and µ using the first r order statistics Y,, ..., Y, from a sample of size n as follows.

(a) Give a formula for the expectation of k: in terms of that for a standard exponential distribution.

(b) Give a formula for the variance of I: in terms of that for a standard exponential distribution

For 11-3 and r=2:

(d) Numerically calculate the coefficients for the BLUES µ and σ*.

(e) Numerically calculate the factors for Var(µ*), Var( σ*), and

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