C given that red shows on the rst three rolls what is

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Unformatted text preview: a constant, even though we don’t know its value. The variable p is random, and therefore the interval p − a p(1−p) n ,p +a p(1−p) n is also random. For example, if a = 5, then, before we start taking the poll, we would have 96% confidence that p will be in this random interval. This interval is not quite suitable for use as a confidence interval, because it depends on the unknown parameter p, so we wouldn’t know the interval. However, p(1 − p) ≤ 0.25 for any p ∈ [0, 1], so if we replace p(1 − p) by 0.25 in defining the confidence interval, it makes the confidence interval larger, and therefore it can only increase the probability that the true parameter is in the interval. In summary, we have: P p∈ a a p − √ ,p + √ 2n 2n ≥1− 1 . a2 (2.12) The larger the constant a is, the greater the probability that p is in the random interval. Table 2.2 shows some possible choices of a and the associated upper bound in (2.10), which is the level of confidence associated with the interval. The confidence interval given by...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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