ME 311 THERMODYNAMICS S. Masutani FALL 2007 Probability Measures—Basic ConceptsConsider a container with three numbered balls: 1, 2, and 3 1 3 2 Perform an experiment: blindfolded, pull out a ball; have an assistant record its number; replace it in the container; repeat the experiment n times; let n →∞. A record of the outcomes could be: Trial 1: 3 Trial 2: 1 Trial 3: 2 Trial 4: 1 Trial n: 1 3 Count the number of times different balls appear and construct a probability measure: 11====∑∑∑tottotiiitottotiiinnnnnnpepeat the experiment with 5 balls, then 10, then 100. If each outcome (ball) is equiprobable: p1= p2= p3= pi= pn= 1/i; pi↓as i ↑ext, consider two containers with 3 balls each. Perform the same experiment: choose one ball from the first container and one ball from the second; record; replace balls; repeat. RNi = 1 2 3 0.333 totiinnp=
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