Question

1. Group of n patients was investigated for carrying some disease. A sequence of indicators of those trials, X_i = (1 for success or 0 if not), is available for n independent patients. Reciprocal probability S = 1/p reflects the number of trials needed to obtain an expected time of a first success. It is necessary to organize staffing to ensure availability of services over that disease in different areas.

1. Provide an unbiased estimation of S based on the record X₁ ,…, X_n .          
2. Provide 95% confidence interval for S if n=9 and 4 patients were infected.

Answer 1

Solution:-

a) The unbiased estimation of S based on the record is 1/p.

The mean is the unbiased estimation of the S based on the record X₁ ,…, X_n .   

b) 95% confidence interval for S if n = 9 and 4 patients were infected is C.I = ( 1.808,2.692).

S.D = 1.6771