Question

In a given population, n individuals are sampled randomly, with replacement, and each sampled individual is asked whether his/her salary is greater than some fixed threshold z. Assume that the salary of a randomly chosen individual has the exponential distribution with unknown parameter λ. Asking whether the salary overcomes a given threshold rather than directly asking for the salary increases the number of people that are willing to answer and decreases the number of mistakes in the collected answers.

Denote by X1,…,Xn the binary responses of the n sampled individuals, so that Xi∈{0,1}. We call the Xi censored data.

Give the parameter of this distribution in terms of λ and z:

Parameter μ(λ)=

Answer 1

ANSWER:

bernoulli with parameter

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