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Lec_14_expected_value

# Lec_14_expected_value - Problem Set 3(reviewed Oct 28 Nov 2...

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1 • Problem Set 3 (reviewed Oct 28 - Nov 2): Chapter 10, pages 290-291: problems 1 and 2 Chapter 11, pages 320-322: problems 3, 4, 8, and 9 • Note: beginning Oct 31, the Monday 4-4:50 section will be led by Michael Sharifi (office hours Wednesdays 1-1:50 in Sequoyah 235) • No class Wednesday, Nov 2 (but discussion sections will meet) Chapter 12: Economics of Information A. Probabilities Suppose we flip a coin 10 times Count 3 heads, 7 tails fraction of heads = 0.30 Try a second time Count 6 heads, 4 tails fraction of heads = 0.60 Third trial: fraction of heads = 0.50 Suppose we try 100 coin flips and count the fraction of heads: • Trial 1 = 0.48 • Trial 2 = 0.54 • Trial 3 = 0.56

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2 Fraction of heads as a function of the number of coin flips 0.5001 0.5011 0.5300 0.5700 0.6000 Trial 4 0.4989 0.5079 0.5430 0.5600 0.5000 Trial 3 0.4980 0.5010 0.5230 0.5400 0.6000 Trial 2 0.5039 0.5012 0.4970 0.4800 0.3000 Trial 1 100,000 10,000 1,000 100 10 number of observations 10 1 10 2 10 3 10 4 10 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Number of observations Fraction of successes Fraction of successes as a function of number of observations (True probability = 0.5, Trial 1) Fraction of successes as a function of number of observations (True probability = 0.5, Trial 2) 10 1 10 2 10 3 10 4 10 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Number of observations Fraction of successes as a function of number of observations (True probability = 0.5, Trial 3) 10 1 10 2 10 3 10 4 10 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Number of observations Conclusions: • When I flip a coin a finite number of n times, I don’t know for sure the fraction of heads • If n is very big, the fraction is going to be very close to 1/2 What’s the fraction of successes look like if true probability of success is 0.8?
3 Fraction of successes as a function of number of observations (True probability = 0.8, Trial 1) 10 1 10 2 10 3 10 4 10

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Lec_14_expected_value - Problem Set 3(reviewed Oct 28 Nov 2...

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