Transcript SIMULATIONS - Texas A&M University
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
ADVANCED SIMULATION – MONTE CARLO METHOD.
FOCUS AND INQUIRY
WHAT IS YOUR FAVORITE VIDEO OR COMPUTER GAME?
WHAT DOES THIS “GAME” HAVE TO KNOW TO PLAY?
WHAT STATISTICS ARE USED?
MAJOR LEAGE BASEBALL 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
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 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
MAKES NO SHOTS—LOSES GAME
MAKES ONE SHOT—TIES GAME AND INTO OVERTIME
MAKES TWO SHOTS—WINS GAME
STATISTICAL INFORMATION
SHAQ IS A 63% FREE THROW SHOOTER
NO OTHER STATISTIC IS NEEDED AT THIS TIME.
SETTING UP A SIMULATION ON THE TI-83+
USING THE PROB/SIM APPLICATION 1.
CHOOSE RANDOM NUMBERS 2.
3.
4.
5.
6.
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
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
AFTER YOU TALLY YOUR SIMULATIONS:
HOW MANY WINS?
HOW MANY TIES?
HOW MANY LOSSES?
WHY HAVE SIMULATIONS
COST/DANGER
NOT MATHEMATICALLY FEASIBLE
NOT PHYSICALLY FEASIBLE
EXAMPLES
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
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.
AN ADVANCED SIMULATION MONTE CARLO SIMULATION
FIND THE AREA OF THE WATER
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?
VIEW THE WAVES
color?
What Is The Area Covered By Blue?
CONT.
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 rectangle 2. if it is within the blue area, record this instance a hit 3. generate a new location and repeat 10,000 times
CALCULATION
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
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
THE SPREADSHEET, PAPER, AND IDEAS WITH TWO VARIABLES ARE TWO DIMINSIONAL.
WHAT ABOUT A 3-D OBJECT?
THREE VARIABLES?
WHAT ABOUT VOLUME?
PROBLEM
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 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) 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 ( 0.9 mm x 0.9 mm)
Geometry Information Particle Interaction Physics
Tasks in Monte Carlo Transport
Random Sampling
Particle Generation Particle Streaming Particle Collisions
Tallies
A SIMULATION JUST LIKE THE SIMPLE ONE
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 1.
2.
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.