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Homework3key - Homework 3(15 points due Feb 3(1 pt 2.42 A...

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1 Homework 3 (15 points) due Feb. 3. (1 pt.) 2.42. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the strain station. Find the probability that John waits for the train a) between 10 and 15 minutes. Since the commuter train leaves every 30 minutes, the maximum wait time is less than 30 minutes. This is equivalent to using geometric probability over the interval [0,30). Note: I am defining my interval as the wait times. The interval could also be defined as the time that John arrives at the station. ? ?±?? ???? ²?????³ 10 ±³´ 15 ??³µ??¶· = ¸¹ 10,15 º¸ ¸¹ 0,30 ·¸ = 5 30 = 1 6 = 0.167 b) at least 10 minutes. ? ?±?? ???? »? ±? ¼?±¶? 10 ??³¶· = ¸¹ 10,30 ·¸ ¸¹ 0,30 ·¸ = 20 30 = 2 3 = 0.667 (2 pt.) 2.44ab. A point is chosen at random in the unit square = {(x,y) : 0 x 1, 0 y 1}. Describe each of the following events in words and determine the probability of each. a) A = {(x,y) : x > 1/3} The event that the x coordinate is greater than 1/3 exclusive, the y coordinate is between 0 and 1. ? ½· = | ¾?¿?±³?¼? ²?????³ À = 0, À = 1, Á = 1 3 , Á = 1)| | µ³?? ¶Âµ±¾? | = 1 2/3 1 = 2 3 = 0.667 b) B = {(x,y) : y 0.7} The event that the y coordinate is less than 0.7 inclusive, the x coordinate is between 0 and 1. ? ÷ = | ¾?¿?±³?¼? ²?????³ À = 0, À = 0.7, Á = 0, Á = 1)| | µ³?? ¶Âµ±¾? | = 1 0.7 1 = 0.7
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2 (1.4 pts.) 2.50. According to the National Vital Statistics Report , there were 4,058,814 live births in the United States in 2000. Of those births, 3,194,005 were to white mothers and 622,598 were to black mothers. a) Use the data to obtain the approximate probability that a live birth in the United States is to a white mother, black mother, other-race mother. ? °???? ?±???²³ = 3194005 4058814 = 0.787, ? ´µ?¶· ?±???²³ = 622598 4058814 = 0.153 ? ¸???² ¹?¶? ?±???²³ = 4058814 3194005 622598 4058814 = 242211 4058814 = 0.060 OR P(Other Race mother) = 1.000 – 0.787 – 0.153 = 0.0060 b) What type of probabilities did you obtain in part (a)? Explain.
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Homework3key - Homework 3(15 points due Feb 3(1 pt 2.42 A...

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