During the last few days before a presidential election, there is a frenzy of voting
intention surveys.On a given day, quite often there are conflicting results from three
major polls.
(a) Think of each of these polls as reporting the fraction of successes (1s) of a Bernoulli random variable , where the probability of success is . Let be the fraction of successes in the sample and assume that this estimator is normally distributed with a mean of and a variance of . Why are the results for all polls different, even though they are taken on the same day?
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