hw2-a

hw2-a - EC305 Economic Statistics Boston University, Fall...

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EC305 – Economic Statistics Boston University, Fall 2010 by Arhan Ertan HW2 – Answers 1. Suppose you roll a pair of dice. Let A be the event that you observe an even number. Let B be the event that you observe a number greater than seven. a. What is the intersection of events A and B ? Answer: [8, 10, 12] b. What is the union of events A and B? Answer: [2, 4, 6, 8, 9, 10, 11, 12] c. What is the complement of event A ? Answer: [3, 5, 7, 9, 11] d. What is AB I ? Answer: [2, 4, 6] e. What is U ? Answer: [2, 3, 4, 5, 6, 7, 8, 10, 12] 2. The probability that interest rates on housing loans will go up in the next 6 months is estimated to be 0.20. The probability that house sales will decrease is estimated to be 0.6. The probability that interest rates will go up and house sales will decrease is estimated to be 0.15. a. The probability that interest rates will go up given that house sales go down is: Answer: 0.15 / 0.6 = 0.25 b. The probability of an increase in interest rates and not a decrease in house sales is: Answer: 0.20 – 0.15 = 0.05 c. The probability of a decrease in house sales and not an increase in interest rates is: Answer: 0.6 – 0.15 = 0.45 d. Are the events of interest rates increasing and house sales decreasing statistically independent or not? Why? Answer: The events of interest rates increasing and house sales decreasing are NOT statistically independent because the joint probability of interest rates increasing and house sales decreasing do not equal the product of the marginal probabilities. 3. A multiple choice quiz has 5 questions, each with 5 answers, A through E . Assume you just guess on all of the questions. a. What is the probability that you guessed on all five questions right? Answer: () ( ) 00032 . 0 5 / 4 5 / 1 5 5 0 5 = C b. What is the probability that you get exactly three questions right? Answer: ( ) 0512 . 0 5 / 4 5 / 1 5 3 2 3 = C 1
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4. A recent marketing survey related consumers’ awareness of a new marketing campaign with their rating of the product. Consumers rated their awareness as low, medium, or high, and rated the product as poor, fair, or good. The results are presented below: Awareness Low Medium High Poor 0.10 0.15 0.07 Rating Fair 0.06 0.11 0.06 Good 0.07 0.11 0.27 a. What is the probability that a consumer had low awareness? Answer: 0.10 + 0.06 + 0.07 = 0.23 b. What is the probability that a consumer who ranked the product as fair had a high awareness of the ad campaign? Answer: 0.06 / (0.06 + 0.11 + 0.06) = 0.26 c. What is the probability that a consumer who had high awareness of the ad campaign ranked the product as good? Answer: 0.27 / (0.07 + 0.11 + 0.27) = 0.675 5. The purchasing agent for a municipality has contracted with a local car dealer to purchase four cars. The dealer has 25 cars on his lot; 10 red, 7 blue, 6 white and 2 purple. If the purchasing agent has no control over the colors he receives, what is the probability that he receives at least one of the purple cars? Answer: P(# of purple cars >= 1) = 1 – P(no purple cars) = 1 – (23/25)*(22/24)*(21/23)*(20/22) = 1 – 0.70 = 0.30 6. The events A and B both have nonzero probabilities. Can A and B be both independent and mutually exclusive?
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This note was uploaded on 11/09/2010 for the course EC EC305 taught by Professor Arahan during the Spring '10 term at BU.

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hw2-a - EC305 Economic Statistics Boston University, Fall...

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