Homework2.pdf - Homework 2 IE 530/STAT 13 1 This question has two parts(a Let X ∼ Negative Binomial(r p Show that µX = r p σX2 = r(1 − p p2(b Let

Homework2.pdf - Homework 2 IE 530/STAT 13 1 This question...

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Homework 2 IE 530/STAT 13 1. This question has two parts. (a) Let X Negative Binomial( r, p ). Show that μ X = r p ; σ 2 X = r (1 p ) p 2 (b) Let X Poisson( λ ). Show that σ 2 X = λ . 2. This question has three parts. (a) Consider a large population with defect ratio of 1%. We draw a large number of samples, each of size 25 and count the number of defective items in each sample. Let D I denote the number of defective items found in sample i , i = 1 , 2 , . . . N , where N 1. Estimate the median, first quartile and third quartile of the sequence D 1 , D 2 , . . . , D n . (b) Let X N( μ = 2 , σ 2 = 0 . 04). Consider a large number of observations of X , that give the values x 1 , . . . , x N , where N 1. Estimate the 12 th percentile of the observations. (c) Consider the Fibonacci sequence given by the recurrence relation F n = F n - 1 + F n - 2 , F (0) = F (1) = 1 . Write the Fibonacci sequence up to n = 15. What percentile of the set of numbers you wrote is the number 21? 3. This question has two parts. (a) Problem 3.10; solve parts (
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  • Fall '97
  • RAVINDRAN
  • Quartile, 1%, $3, Fibonacci number, ten minutes

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