答案和详解如下： 1、The probability density function of a continuous uniform distribution is best described by a: A) vertical line segment. B) horizontal line segment. C) line segment with a 45-degree slope. D) line segment with a curvilinear slope. The correct answer was B) By definition, for a continuous uniform distribution, the probability density function is a horizontal line segment over a range of values such that the area under the segment (total probability of an outcome in the range) equals one. 2、A discount brokerage firm states that the time between a customer order for a trade and the execution of the order is uniformly distributed between three minutes and fifteen minutes. If a customer orders a trade at 11:54 A.M., what is the probability that the order is executed after noon? A) 0.500. B) 0.125. C) 0.750. D) 0.250. The correct answer was C) The upper and lower limits of the uniform distribution are three and 15. Since the problem concerns time, it is continuous. Noon is six minutes after 11:54 A.M. The probability the order is executed after noon is (15 - 6) / (15 - 3) = 0.75. 3、A random variable follows a continuous uniform distribution over 27 to 89. What is the probability of an outcome between 34 and 38? A) 0.0546. B) 0.0645. C) 0.0719. D) 0.0620. The correct answer was B) P(34 ≤ X ≤ 38) = (38 - 34) / (89 - 27) = 0.0645 4、Consider a random variable X that follows a continuous uniform distribution: 7 ≤ X ≤ 20. Which of the following statements is least accurate? A) F(21) = 0.00. B) F(10) = 0.23. C) F(12 ≤ X ≤ 16) = 0.307. D) F(6) = 0. The correct answer was A) F(21) = 1.00 The probability density function for a continuous uniform distribution is calculated as follows: F(X) = (X – a) / (b – a), where a and b are the upper and lower endpoints, respectively. (If the given X is greater than the upper limit, the probability is 1.0.) Shortcut: If you know the properties of this function, you do not need to do any calculations to check the other choices. The other choices are true. §
F(10) = (10 – 7) / (20 – 7) = 3 / 13 = 0.23 §
F(12 ≤ X ≤ 16) = F(16) – F(12) = [(16 – 7) / (20 – 7)] - [(12 – 7) / (20 – 7)] = 0.692- 0.385 = 0.307 §
F(6) = 0 (if the given X is less than the lower limit, the probability is 0) | 
发表于 2008-4-10 14:13
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