HW3solutions2008 - STATISTICS 408 HOMEWORK#3 SOLUTION...

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STATISTICS 408 HOMEWORK #3: SOLUTION Problem 1. The physician claims that the probability that a patient has a viral infection is 95%. What does this statement mean (provide an operational definition for this measure)? Is this a property of the individual? Solution. This means that among all other patients with similar symptoms and a similar health background, 95% of them have had the viral infection. An operational definition would be P (Disease) = #diseased/ #similar This is a property of a collective of individuals, not the individual patient. Problem 2. In the Monte Hall Game, explain why the strategy to switch has probability 2/3rds of winning. Solution. Without a loss of generality, suppose the car is behind door 3. If we choose door 1, we’ll be shown the goat behind door 2, and we’ll switch to door 3 and WIN. Similarly, if we choose door 2, we’ll be shown the goat behind door 3, and we’ll switch to door 3 and WIN. If we choose door 3, we’ll be shown either of the two goats, switch to the goat we were not shown, and LOSE. Thus, 2 out of 3 options are a WIN, but 1 of the three options is a loss, so the chance of winning is 2/3 . Problem 3. Define the symbols P (A |B), P (B|A), P (A and B), P (A or B), and P (not A). Provide examples of each. Solution. P (A |B) = ”Among those with characteristic B, the proportion who also have characteristic A” Example: The proportion of a woman earning a promotion is P (promotion |woman) P (B|A) = ”Among those with characteristic A, the chance of also having characteristic B” Example: Among those who received a promotion, the proportion who were women is P (woman |promotion) P (A and B) = ”The proportion of units in a population with characteristic A and B” Example: The proportion of employees in company X who are both a woman and received a promotion is P (woman and promotion) P (A or B) = ”The proportion of units in the population that possess either characteristic A or B or both” Example: The proportion of a people in a company X who are either a woman or received a promotion is P (woman or promotion) P (not A) = ”The proportion of units in the population that do not possess characteristic A”
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  • Spring '08
  • ROTHMAN
  • Statistics, Probability, Probability theory, Stochastic process, Type I and type II errors, Shoplifting

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