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=∞