In surveys about sensitive topics, respondents are sometimes given ways to “hide” their answers from the surveyor. In a survey of taxpayers, one of the questions is, “Did you cheat on your taxes?” To answer, the respondent is asked to toss a coin. If it lands heads, the respondent must answer “yes.” If it lands tails, the respondent must answer the question truthfully, either “yes” or “no” (the answer has to be the one that is true). Assume that all respondents follow this procedure, and that for 10% of the respondents the truthful answer is “yes.” Also assume that the result of a respondent’s
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A gambling game pays 4 to 1 and the chance of winning is 1 in 6. Suppose you bet $1 on this game 600 times independently. Find the expected number of times you win. Find the SE of the number of times you win. Find the chance that you lose more than $50 (that is, your net gain in the 600 bets is less than -$50).