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Published byDenis Watkins Modified over 9 years ago
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Section 5.3 – basics of simulation Simulation – the imitation of chance behavior, based on a model that accurately reflects the experiment under consideration – an effective tool for finding likelihoods of complex results once we have a trustworthy model. – Gives us good estimates of probabilities
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Steps of Simulation 1)State problem or describe experiment 2)State the assumption 3)Assign digits to represent outcomes 4)Simulate many repetitions
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State the problem or describe theexperiment. – Toss a coin 10 times. – What is the likelihood of a run of at least 3consecutive heads or 3 consecutive tails? State the assumptions – A head or tail is equally likely to occur oneach toss – Tosses are independent of each other What happens on one toss does not influencethe next toss
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Assign digits to represent outcomes. – One digit simulates one toss of a coin – Odd digits represent heads; even represent tails. Simulate many repetitions. – Look at 10 consecutive digits in Table B simulates one repetition – 19223 95034 05756 28713 96409 12531 – hhh hhh t tt hhh ttt hhh – Repeated 25 total times, 23 had a run of 3 or more State your conclusions. – Estimate probability of run by proportion – 23/25 = 0.92
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Assigning Digits Choose a person at random from a group of which 70% are employed. One digit simulates one person. – 0, 1, 2, 3, 4, 5, 6 = employed – 7, 8, 9 = not employed – 1, 2, 3, 4, 5, 6, 7 = employed – 8, 9, 0 = not employed – 00, 01, 02,…69 = employed – 70, 71, 72,…99 = not employed – 01, 02, 03,…70 = employed – 71, 72, 73,…99, 00 = not employed – Good Options? Bad Options?
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Assigning Digits more practice… Choose on person at random from a group of which 73% are employed. – Now 2 digits are needed to simulate one person – 00, 01, 02, …, 72 = employed – 73, 74, 75, …, 99 = not employed – 01, 02, 03, …, 73 = employed – 74, 75, 76, …, 99, 00 = not employed
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Assigning Digits even more practice… Choose one person at random from a group 50% employed, 20% unemployed, and 30% are not in the labor force. – 0, 1, 2, 3, 4 = employed – 5, 6 = unemployed – 7, 8, 9 = not in work force – 1, 2 = unemployed – 3, 4, 5 = not in labor force – 6, 7, 8, 9, 0 = employed – Lots of options here!
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Frozen yogurt sales State the problem. – Simulate 10 fro yo sales based on the recent history of 38% Chocolate, 42% Vanilla, 20% Strawberry State the assumptions – The pairs of digits on the random digit Table B are independent of each other Assign digits – 01, 02, … 38 = Chocolate (C) – 39, 40, … 80 = Vanilla (V) – 81, 82, … 99, 00 = Strawberry (S) – There are other options here!
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Simulate – Start at line 133 – 45740 41807 65561 33302 – V V C C C V V C C C Conclusions
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Randomizing with the Calculator randInt – TI 83 – MATH/PRB/5:randInt – TI 89 – Catalog / F3 (flash apps) – randInt (1, 6, 8) Rolling a die 8 times – randInt (0, 99, 12) Choosing 12 two digit numbers between 00 and 99 – randInt (1, 2, 10) Flipping a coin 10 ten times
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