答案和详解如下： Q1. Which of the following qualifies as a cumulative distribution function? A) F(1) = 0, F(2) = 0.5, F(3) = 0.5, F(4) = 0. B) F(1) = 0.5, F(2) = 0.25, F(3) = 0.25. C) F(1) = 0, F(2) = 0.25, F(3) = 0.50, F(4) = 1. Correct answer is C) Because a cumulative probability function defines the probability that a random variable takes a value equal to or less than a given number, for successively larger numbers, the cumulative probability values must stay the same or increase. Q2. A random variable X is continuous and bounded between zero and five, X 0 ≤ X ≤ 5). The cumulative distribution function (cdf) for X is F(x) = x / 5. Calculate P(2 ≤ X ≤ 4). A) 0.40. B) 1.00. C) 0.50. Correct answer is A) For a continuous distribution, P(a ≤ X ≤b) = F(b) − F(a). Here, F(4) = 0.8 and F(2) = 0.4. Note also that this is a uniform distribution over 0 ≤ x ≤ 5 so Prob(2 < x < 4) = (4 − 2) / 5 = 40%. | 
发表于 2009-1-9 10:18
| 
