SIMULATIONS by 4fU3n81

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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
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. DRAW TWO
3. RANGE: 0-99
4. REPEAT YES
5. SET #’S 0-62 AS A POINT. (63 #’s)
6. 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)
              Tasks in Monte Carlo
                   Transport
                   Random Sampling
                      Particle
                     Generation
 Geometry
Information
                      Particle
                     Streaming       Tallies



                      Particle
  Particle           Collisions
Interaction
  Physics
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. DESCRIBE HOW THE MONTE
   CARLO SIMULATION COULD BE
   USED TO RADIATE CANCER
   CELLS AND WHY?
2. DESCRIBE HOW THE MONTE
   CARLO SIMULATION COULD BE
   USED IN THREE OTHER
   SITUATIONS AND EXPLAIN.
   GOODBYE
THIS SIMULATED
 CLASSROOM IS
  NOW OVER!

								
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