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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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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
Steps of Simulation • State problem or describe experiment • State the assumption • Assign digits to represent outcomes • Simulate many repetitions
State the problem or describe the experiment. • Toss a coin 10 times. • What is the likelihood of a run of at least 3 consecutive heads or 3 consecutive tails? • State the assumptions • A head or tail is equally likely to occur on each toss • Tosses are independent of each other • What happens on one toss does not influence the next toss
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 • hhhhhhttthhhttthhh • 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
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?
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
Assigning Digits evenmore 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!
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!
Simulate • Start at line 133 • 45740 41807 65561 33302 • 45 74 04 18 07 65 56 13 33 02 • V V C C C V V C C C • Conclusions
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
examples • #59. state how you would use the following aids to establish a correspondence in a simulation that involves a 75% chance • A coin • A six-sided die • A random digit table • A standard deck of playing cards.
