By Trosset M.W.

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**Additional info for Introduction to statistical inference and data analysis**

**Sample text**

Yet in the first situation, which mimics a lottery, more than 70% of people asked chose to go for the $5000. ”3 The author evidently considered the reported preferences paradoxical, but are they really surprising? Plus or minus $5 will not appreciably alter the financial situations of most subjects, but plus or minus $5000 will. It is perfectly rational to risk a negligible amount on the chance of winning $5000 while declining to risk a negligible amount on the chance of losing $5000. The following examples further explicate this point.

Thus, the probability of a false positive is P (+|D c ) and the probability of a false negative is P (−|D). 2 Now suppose that a randomly selected patient has a positive ELISA test result. Obviously, the patient has an extreme interest in properly assessing the chances that a diagnosis of HIV is correct. This can be expressed as P (D|+), the conditional probability that a patient has HIV given a positive ELISA test. This quantity is called the predictive value of the test. M. Sloan et al. (1991), “HIV Testing: State of the Art,” Journal of the American Medical Association, 266:2861–2866.

Hence, 5 · 1. #(A ∩ B) = 3 Thus, P (A ∪ B) = 5 3 · 52 + 5 2 65 · 53 − 5 3 = 1490 . 1916. 65 Example 5 (The Birthday Problem) In a class of k students, what is the probability that at least two students share a common birthday? As is inevitably the case with constructing mathematical models of actual phenomena, some simplifying assumptions are required to make this problem tractable. e. we ignore February 29. Then the sample space, S, of possible birthdays for k students comprises 365k outcomes.