STAT3021 PPT2 Solution.pdf

STAT3021 PPT2 Solution.pdf - STAT 3021 Chapter 2...

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STAT 3021 Chapter 2. Probability 2.1, 2.2 Sample Space and Events Definition 1. The set of all possible outcomes of a statistical experiment is called the sample space and is represented by the symbol S . Example 1. a. Rolling a die and observe the number it shows on the top face. Then S = { 1 , 2 , 3 , 4 , 5 , 6 } b. Rolling two dice and observe the two numbers they show. Then S = { (1 , 1) , (1 , 2) , (1 , 3) , ... (6 , 5) , (6 , 6) } c. Rolling two dice and calculate the sum of the two numbers. Then S = { 2 , 3 , 4 , 5 , 6 , ..., 12 } Example 2. Suppose that we randomly select a student from class and ask a question. In the below situation, describe the sample space for the experiment. a. How much time (in hours) did the student spend studying during the last 24 hours? S = [0 , 20] b. In what state was the student born, given that he/she was born in the U.S.? S = { AL, AK, AZ, ..., WY } c. How many friends does the student have? S = { 0 , 1 , ... } In some experiment it is helpful to list the elements of the sample space systemically by means of a tree diagram. Example 3. An experiment consists of flipping a coin and then flipping it a second time if a head occurs. If a tail occurs on the first flip, then a die is tossed once. To list the elements of the sample space providing the most information, we construct the tree diagram below.
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