Optimum grouped exponential for problem 93 suppose that all, Ask an Expert

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Optimum grouped exponential. For Problem 9.3, suppose that all I units have a common time T~ between inspections; that is,

(a) Derive an explicit formula for the ML estimate 6; use part (b) of Problem 9.3.

(b) Derive the formula for the true asymptotic variance of 6; use part (h) of Problem 9.3.

(c) Derive the optimum time T? that minimizes the true asymptotic variance. It is a multiple cJ of the true unknown Numerically find c, for J = 2,3.

(d) Evaluate the minimum variance for T, = T: and compare it with the variance of 4 for a complete observed sample.

(e) In practice, one must guess a value Calculate and plot on log-log paper for J = 2.

(f) Explain how to use "exact" confidence limits for the parameter p of a geometric distribution (Chapter 2) to get exact limits for θ, when J=∞

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