## Class 30: Randomized Response

### Discussion

We would like to talk about the paradox from the class handout about a week ago. It went like this:

Your uncle presents you with two sealed envelopes on your birthday, and tells you each of them contains a check. He says that one check is for twice as much money as the other, and lets you chose which envelope you want. You make your choice and find that the check inside is for \$20.

Your uncle now asks you if you would like to switch envelopes. Having taken an introductory statistics class, you reason as follows. The other envelope is equally likely to contain \$40 or \$10. Therefore, the expected value for the other envelope is (\$40 + \$10)/2, or \$25. Should you switch?

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Here is a method for taking a class survey on a sensitive subject:

Everyboody in the class should flip a coin twice, privately, so that no one sees the results. People who get a head on the first flip should answer 'yes' or 'no' to the sensitive question. People who get a tail on the first flip should answer 'yes' or 'no' to the innocuous question "Were both your flips the same?". We can use the proportion of 'yes' responses to estimate the answer to the sensitve question.

### Homework Assignment for Monday, May 1

Read Chapters 27, 28, and 29 in FPPA. Do review exercises 1, 2, 3, 5 for Chapter 28 and review exercises 1, 4, 7, 12 for Chapter 29.

### Journal Assignment

Pick two questions from the risk quiz (from last time) for which you think it's possible to estimate the risks. How would you make the estimates?