100AHW2 - STAT 100A HWII Due next Wed in class Problem 1:...

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Unformatted text preview: STAT 100A HWII Due next Wed in class Problem 1: If we flip a fair coin n times independently, what is the probability that we observe k heads? k = 0, 1, ..., n. Please explain your answer. Problem 2: Prove the following two identities: (1) P (A|B) = 1 - P (A|B). (1) P (A B|C) = P (A|C) + P (B|C) - P (A B|C). Problem 3: Independence. If P (A|B) = P (A), prove (1) P (A B) = P (A)P (B). (2) P (B|A) = P (B). Problem 4: Prove the following two identities (C stands for cause, E stands for effect). (1) Rule of total probability: P (E) = P (E|C)P (C) + P (E|C)P (C). (2) Bayes rule: P (C|E) = P (C)P (E|C)/[P (C)P (E|C) + P (C)P (E|C]. Problem 5: Suppose 1% of the population is inflicted with a particular disease. For a medical test, if a person has the disease, then 95% chance the person will be tested positive. If a person does not have the disease, then 90% chance the person will be tested negative. Using precise notation, calculate (1) The probability that a randomly selected person will be tested positive. (2) If the person is tested positive, what is the chance that he or she has the disease? If the person is tested negative, what is the chance that the person has no disease? 1 ...
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This note was uploaded on 08/24/2009 for the course MATH 262447221 taught by Professor Weisbart during the Spring '09 term at UCLA.

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