2 Differential Privacy When evaluating the frequency of stigmatized, private, illegal, or embarrassing activities, the randomized response approach is a simple yet effective way of achieving differential privacy. In this problem, you'll explore and show some useful properties of randomized responses. Suppose we are interested in assessing drug use in Berkeley, and to this end we conduct a survey to estimate the fraction of the population that regularly uses drugs. However, this is a sensitive question: people may not feel comfortable at disclosing this type of information. In the survey, each participant is asked: \"Do you normally use drugs at least once a week?\". To achieve randomized responses, the participant is then instructed to respond as follows: 1. Flip a fair coin (326., 50% chance of heads and 50% chance of tails). 2. If tails, then respond truthfully. 3. If heads, then ip the coin again. Respond \"Yes\" if heads, and \"No\" if tails. (d) (2 points) Suppose you take the sample mean of the survey responses and get a value A = i211 b;. Using the fact in Equation (1), propose an estimator for q, the true fraction of the population that frequently uses drugs. Your solution should be in terms of A and constants