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SIMULATIONS. Simulations are used by engineers, programmers, and other scientists to produce the probable results of an experiment or happening. COMING EVENTS. SIMULATIONS IN GAMES. SIMULATIONS OF EVENTS OR FUTURE ACTIONS. SETTING UP SIMPLE SIMULATIONS

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### Simulations are used by engineers, programmers, and other scientists to produce the probable results of an experiment or happening.

### SETTING UP A SIMULATION ON THE scientists to produce the probable results of an experiment or happening.TI-83+

### AN ADVANCED SIMULATION scientists to produce the probable results of an experiment or happening.

COMING EVENTS scientists to produce the probable results of an experiment or happening.

- SIMULATIONS IN GAMES.
- SIMULATIONS OF EVENTS OR FUTURE ACTIONS.
- SETTING UP SIMPLE SIMULATIONS
- ADVANCED SIMULATION –MONTE CARLO METHOD.

FOCUS AND INQUIRY scientists to produce the probable results of an experiment or happening.

- WHAT IS YOUR FAVORITE VIDEO OR COMPUTER GAME?
- WHAT DOES THIS “GAME” HAVE TO KNOW TO PLAY?
- WHAT STATISTICS ARE USED?

MAJOR LEAGE BASEBALL scientists to produce the probable results of an experiment or happening.SAMMY SOSA EDITION

- WHAT ARE THE STATISTICS FOR THE PITCHER: ERA, STRIKEOUT RATE…
- WHAT ARE THE STATISTICS FOR THE BATTER: BATTING AVERAGE, HOW BATTER DOES AGAINST CERTAIN PITCHER…
- IS THE BAT CORKED?

GAME SIMULATION scientists to produce the probable results of an experiment or happening.

- THE COMPUTER TAKES ALL OF THE INFORMATION (IN STATISTICAL FORM AND CALCULATES THE PROBABILITY OF AN EVENT HAPPENING.
- THE COMPUTER WILL CHOOSE WHAT WILL HAPPEN TO THE PLAYERS BY PROBABILITY.

SIMPLE SIMULATION scientists to produce the probable results of an experiment or happening.

SITUATION:

- THE LAKERS ARE ONE POINT BEHIND.
- SHAQ IS FOULED WITH NO TIME LEFT ON THE CLOCK (TWO FREE THROWS)
- RUN 25 SIMULATIONS AND GIVE RESULTS

POSSIBILITIES scientists to produce the probable results of an experiment or happening.

- MAKES NO SHOTS—LOSES GAME
- MAKES ONE SHOT—TIES GAME AND INTO OVERTIME
- MAKES TWO SHOTS—WINS GAME

STATISTICAL INFORMATION scientists to produce the probable results of an experiment or happening.

- SHAQ IS A 63% FREE THROW SHOOTER
- NO OTHER STATISTIC IS NEEDED AT THIS TIME.

USING THE PROB/SIM APPLICATION scientists to produce the probable results of an experiment or happening.

- CHOOSE RANDOM NUMBERS
- DRAW TWO
- RANGE: 0-99
- REPEAT YES
- SET #’S 0-62 AS A POINT. (63 #’s)
- SET #’S 63-99 AS A MISS. (37 #’s)

USING THE RANDOM NUMBER FUNCTION scientists to produce the probable results of an experiment or happening.

- FIND THE RANDOM INTEGER FUNCTION: MATH-PRB #5
- randInt (min#, max#, amount generated)
- randInt (0, 99, 2)—(1, 100, 2) will also work.
- SET UP PARAMETERS AS IN PROB/SIM.
- KEEP PRESSING ENTER 25 TIMES AND TALLY

TALLY TIME scientists to produce the probable results of an experiment or happening.

- AFTER YOU TALLY YOUR SIMULATIONS:
- HOW MANY WINS?
- HOW MANY TIES?
- HOW MANY LOSSES?

WHY HAVE SIMULATIONS scientists to produce the probable results of an experiment or happening.

- COST/DANGER
- NOT MATHEMATICALLY FEASIBLE
- NOT PHYSICALLY FEASIBLE

EXAMPLES scientists to produce the probable results of an experiment or happening.

- BOMBING OF IRAN (IRAQ EARLIER)
- DAMAGE DUE TO A POSSIBLE HURRICANE TO THE MIAMI AREA
- DAMAGE DUE TO A NUCLEAR EXPLOSION ON NEW YORK CITY
- FINDING THE POSSIBLE PROFIT WHEN A SALES CAMPAIGN IS STARTED

GUIDED PRACTICE scientists to produce the probable results of an experiment or happening.

BUILD SIMULATIONS FOR THE FOLLOWING: RUN 25 SIMULATIONS FOR EACH:

- THE WEATHERMAN STATES THERE IS A 65% CHANCE OF RAIN NEXT FRIDAY—WILL IT RAIN FOR THE JULY 4 PARADE.
- THE SCHOOL POPULATION IS AS FOLLOWS: 43% WHITE; 37% HISPANIC; 15% BLACK; AND 5% OTHER. A COMMITTEE IS BEING FORMED –WHAT IS THE RACIAL COMPOSITION OF THE COMMITTEE—IF 12 MEMBERS ARE CHOSEN.

MONTE CARLO SIMULATION

FIND THE AREA OF THE WATER scientists to produce the probable results of an experiment or happening.

To further understand Monte Carlo simulation, let us examine a simple problem. Below is a rectangle for which we know the length [10 units] and height [4 units]. It is split into 2 sections which are identified using different colors. What is the area covered by the blue color?

color? scientists to produce the probable results of an experiment or happening.

What Is The Area Covered By Blue?

VIEW THE WAVESCONT. scientists to produce the probable results of an experiment or happening.

Due to the irregular way in which the rectangle is split, this problem is not easily solved using analytical methods. However, we can use Monte Carlo simulation to easily find an approximate answer. The procedure is as follows: 1. randomly select a location within the rectangle2. if it is within the blue area, record this instance a hit3. generate a new location and repeat 10,000 times

CALCULATION scientists to produce the probable results of an experiment or happening.

BLUE AREA= # HITS x 40 UNITS

10,000

THIS CAN ALSO BE USED IN MS EXCEL USING CELLS AS POINTS OF CHOOSING BY THE COMPUTER.

THERE ARE MANY DIFFERENT TYPES OF SOFTWARE THAT CAN CALCULATE THIS

MONTE CARLO PRACTICE scientists to produce the probable results of an experiment or happening.

- DESCRIBE HOW A MONTE CARLO SIMULATION WOULD WORK TO DISCOVER THE PERCENTAGE OF WATER ON THE EARTH’S SURFACE.
- USING 10,000 TRYS—HOW CAN YOU FIND THE RACIAL PERCENTAGE OF THE POPULATION OF NEW YORK CITY.

HOW ABOUT 3-D scientists to produce the probable results of an experiment or happening.

- THE SPREADSHEET, PAPER, AND IDEAS WITH TWO VARIABLES ARE TWO DIMINSIONAL.
- WHAT ABOUT A 3-D OBJECT?
- THREE VARIABLES?
- WHAT ABOUT VOLUME?

PROBLEM scientists to produce the probable results of an experiment or happening.

- HOW TO YOU KEEP AN APPLE FRESH ON THE SHELF OF A GROCERY STORE.
- IF IT SITS TOO LONG IT BECOMES SOFT AND MUSHY—NOT GOOD FOR SALES.
- IRRADIATION WILL PRESERVE THE APPLE FOR A LONGER SHELF LIFE.

APPLE IRRADIATION scientists to produce the probable results of an experiment or happening.

MORE PROBLEMS

- APPLE IS NOT UNIFORM THOUGH ITS SOLID STATE
- SKIN OR PEEL IS THICKER
- SEEDS
- CORE
- UNDER PEEL IS DIFFERENT DENSITY THAN NEAR CORE

Computer Tomography (CT) scientists to produce the probable results of an experiment or happening.

Slice thickness

- 1,3,5 mm
Cross-sectional resolution

0.2 mm x 0.2 mm

CT number

- Water = 0
- Air = -1000

A slice image of an apple scientists to produce the probable results of an experiment or happening.( 0.9 mm x 0.9 mm)

Tasks in Monte Carlo Transport scientists to produce the probable results of an experiment or happening.

Random Sampling

Particle

Generation

Geometry

Information

Tallies

Particle

Streaming

Particle

Interaction

Physics

Particle

Collisions

A SIMULATION JUST LIKE THE SIMPLE ONE scientists to produce the probable results of an experiment or happening.

- THIS SIMULATION IS RUN BY EITHER PARALLEL COMPUTERS OR A VERY POWERFUL ONE
- DATA IS GIVEN ON HOW IS THE BEST WAY TO IRRADIATE THE FRUIT

PRACTICE scientists to produce the probable results of an experiment or happening.

- DESCRIBE HOW THE MONTE CARLO SIMULATION COULD BE USED TO RADIATE CANCER CELLS AND WHY?
- DESCRIBE HOW THE MONTE CARLO SIMULATION COULD BE USED IN THREE OTHER SITUATIONS AND EXPLAIN.

GOODBYE scientists to produce the probable results of an experiment or happening.

THIS SIMULATED CLASSROOM IS NOW OVER!

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