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 1)State problem or describe experiment 2)State the assumption 3)Assign digits to represent outcomes 4)Simulate many repetitions

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

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 – – 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

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 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!

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 – – 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