2014-Quiz 1 Solutions - Statistical Analysis Quiz 1 Section 510.601.52 In a recent survey of Baltimore homes 10 of the homes have a deck and 52 have a

2014-Quiz 1 Solutions - Statistical Analysis Quiz 1 Section...

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Statistical Analysis Quiz 1 Section : 510.601.52 In a recent survey of Baltimore homes, 10% of the homes have a deck and 52% have a parking space. Suppose 91% of the homes with a deck also have a parking space. a. What percent of homes have a deck and a parking space? (3 points) P ( P∩ D ) = P ( P | D ) P ( D ) = 0.91 0.1 = 0.091 b. What is the probability that a home has a deck or a parking space? (3 points) P ( P D ) = P ( P ) + P ( D ) P ( P∩ D ) = 0.52 + 0.1 0.091 = 0.529 c. What is the probability that a home with a parking space has a deck? (4 points) P ( D | P ) = P ( D∩ P ) P ( P ) = P ( P | D ) P ( D ) P ( P ) = 0.91 0.1 0.52 d. Are the events "having a deck" and "having a parking space" independent? Why or why not? (3 points) If independent, P ( P∩ D ) = P ( P ) P ( D ) ; P ( P∩ D ) = 0.091 ; P ( P ) P ( D ) = 0.52 0.1 = 0.052 , hence the two are not independent
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Statistical Analysis Quiz 1 Section : 510.601.F2 -1 We observed fluctuations in the value of the US dollar against the Euro on 4 random days in 2014. On each of the days, we took an equal number of measurements. On day 1, 2% of the measurements showed depreciation of the dollar against the euro, 4% of measurements on day 2 showed depreciation, and 1% on day 3 while 6% of the measurements showed depreciation on day 4. a. If a certain measurement is selected from each day, what is the probability that the measurements from days 1 and 2 showed depreciation and from days 3 and 4 did not show depreciation? (3 points) P ( 1 2 ´ 3 ´ 4 ) = 0.02 0.04 0.99 0.94 b. What is the probability that a randomly selected measurement is from day 2 and showed depreciation? (3 points) P ( Depreciation∩ 2 ) = P ( Depreciation | 2 ¿ P ( 2 ) = 0.04 0.25 c. If a randomly selected measurement showed depreciation, what is the probability that it came from day 2? (4 points) P ( Depreciation | 2 P ( Depreciation | 1 P ( 2 | Depreciation ) = ¿ P ( 2 ) ¿ ¿ P ( 1 ) + P ( Depreciation | 2 ¿ P ( 2 ) + P ( Depreciation | 3 ¿ P ( 3 ) + P ( Depreciation | 4 ¿ P ( 4 ) ¿ = 0.02 2. Four six-sided dice are rolled. What is the probability that the numbers they show are all different? (3 points)
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6 ( withoutrepitition ) P 4 6 ( repitition ) = 6 ! 2 ! 6 4 the days, we took an equal number of measurements. On day 1, 2% of the measurements showed depreciation of the dollar against the euro, 4% of measurements on day 2 showed depreciation, and 1% on day 3 while 6% of the measurements showed depreciation on day 4. a. If a certain measurement is selected from each day, what is the probability that the measurements from days 1 and 2 did not show depreciation and from days 3 and 4 showed depreciation? (3 points) P ( ´ 1 ´ 2 3 4 ) = 0.98 0.96 0.01 0.06 b. What is the probability that a randomly selected measurement is from day 3 and showed depreciation?
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