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Unformatted text preview: M4056 Lecture Notes. August 30, 2010 Section 5.1. A basic task of statistics is to obtain knowledge of a population from observations of samples. To make the process rigorous, we create a probabilistic model of a random sample. A random sample of size n is modeled by a collection of random variables X 1 , . . ., X n that are mutually independent an all have the same distribution, f . Such a collection is said to be iid independent and identically distributed. Examples: 1. We take n beads from a large jar and observe whether the color is red or not. Let X i = 0 if the i th bead is not red and let X i = 1 if it is red. In a random sample, we expect the colors of the beads other than the i th have no influence on the color of the i th , and we expect the probability of being red to be the same for all i . (If we drew beads without replacement from a small jar, then we would violate the assumptions badly.) 2. For each possible height range, there is a definite probability of a random LSU student2....
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This note was uploaded on 11/29/2011 for the course MATH 4056 taught by Professor Staff during the Fall '08 term at LSU.
- Fall '08