04_01 - Random Variables p. 4-1 A Motivating Example...

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p. 4-1 Random Variables • A Motivating Example Experiment: Sample k students without replacement from the population of all n students (labeled as 1, 2, …, n , respectively) in our class. = {all combinations} = {{ i 1 , …, i k }: 1 i 1 < < i k n } A probability measure P can be defined on , e.g, when there is an equally likely chance of being chosen for each students, For an outcome , the experimenter may be more interested in some quantitative attributes of , rather than the itself, e.g., The average weight of the k sampled students The maximum of their midterm scores The number of male students in the sample Q : What mathematical structure would be useful to characterize the random quantitative attributes of ’s? p. 4-2 • Definition: A random variable X is a function which maps the sample space to the real numbers R , i.e., X : R . The P defined on would be transformed into a new probability measure defined on R through the mapping X the outcome of X is random, but the map X is deterministic Example (Coin Tossing): Toss a fair coin 3 times, and let X 1 = the total number of heads X 2 = the number of heads on the first toss X 3 = the number of heads minus the number of tails ={ hhh , hht , hth , thh , htt , tht , tth , ttt } R R R
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This note was uploaded on 02/15/2012 for the course MATH 2810 taught by Professor Shao-weicheng during the Fall '11 term at National Tsing Hua University, China.

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04_01 - Random Variables p. 4-1 A Motivating Example...

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