Question: Kuk (1990) proposed the following randomized response method. Ask the respondent to generate two independent binary variables X1 and X2 with P (X1 = 1)

Kuk (1990) proposed the following randomized response method. Ask the respondent to generate two independent binary variables X1 and X2 with P (X1 = 1) = θ1 and
P(X2 = 1) = θ2. The probabilities θ1 and θ2 are known. Now ask the respondent to tell you the value of X1 if she is in the sensitive class, and X2 if she is not in the sensitive class. Suppose the true proportion of persons in the sensitive class is pS.
a. What is the probability that the respondent reports 1?
b. Using your answer to (a), give an estimator ṔS of pS. What conditions must θ1 and θ2 satisfy?
c. What is V (ṔS) if an SRS is taken?

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