Term 1 Simulation maths

Question 1

What is simulation?

Answer 1

The imitation of the operation of a real- world process or system overtime.

Question 2

Probability calculation

Answer 2

Collecting data to run a simulation to come up with a more accurate prediction.

Question 3

PPDAC investigation cycle

Answer 3

To investigate simulations

Question 4

Problem Kaupapa

Answer 4

Investigation question

Question 5

Plan/ whakamahere

Answer 5

Select tool
-define a trial
-number of trials
-Simulation versus real world

Question 6

Data/ Raraunga

Answer 6

-Generate simulated data

Question 7

Analysis/Tātari

Answer 7

-draw graphs
-Summary statistics
-Features

Question 8

Conclusion/ whakatau

Answer 8

-Answer investigation question

Question 9

Problem

Answer 9

Defining the real world problem

Question 10

Probability that an event occurs

Answer 10

One of the two types of investigation questions

Question 11

Mean or average number of times that an event occurs

Answer 11

One of the two types of investigation questions

Question 12

Example situation

Answer 12

When playing basketball and doing a penalty shootout the player gets three shots at a goal

Question 15

Example probability question

Answer 15

If a basketball player is doing a penalty shoot out what is the probability that the player makes all three shot shots?

Question 16

Example mean or average question

Answer 16

If a basketball player takes a penalty shoot out what is the average number of shots out of three the player will make?

Question 17

Example situation

Answer 17

Miss is interested in different eye colours that any POTENTIAL children of hers may have. The probability of one child having blue eyes is 0.7.

Question 18

Example probability question

Answer 18

If miss has four children what is the probability that three of her children have blue eyes?

Question 19

Example mean or average question

Answer 19

What is the average number of children miss has to have before she has two children in a row (one after the other) that have blue eyes?

Question 20

Sample space

Answer 20

A list of all the possible outcomes of an experiment. E.G-a dice

Question 21

Sample space

Answer 21

All possible outcomes

Question 22

Each outcome has a single probability

Answer 22

All probabilities must add up to one

Question 23

Probability of blue eyes equals 0.7.

Answer 23

To match the blue eyes I want seven random numbers because 7/10 equals 0.7

Question 24

0.3+0.4+0.2+0.1=1

Answer 24

All the probabilities add up to1
-Blue eyes 0.3
-Brown eyes 0.4
-Green eyes 0.2
-Grey eyes 0.1

Question 25

0.3

Answer 25

3/10

Question 26

2/10

Answer 26

0.2

Question 27

Simulation with one decimal place example: 0.2

Answer 27

Generate 10 random numbers and allocate these to the outcomes

Question 28

If you are simulating to 2 decimal places example: 0.45

Answer 28

Then generate 100 random numbers and allocate these to the outcomes

Question 29

Outcome =blue eyes Probability =0.3 What is random number matching?

Answer 29

Random number matching: 1,2,3

Question 30

Outcome =brown eyes Probability =0.4 What is random number matching

Answer 30

Random number matching: 4,5,6,7

Question 31

Outcome= green eyes Probability = 0.2 What is random number

Answer 31

Random number matching: 8,9

Question 32

Outcome = grey eyes Probability =0.1 What is random number matching?

Answer 32

Random number match: 10

Question 33

=RANDBETWEEN (minimum, maximum)

Answer 33

The RANDBETWEEN formula will generate a random(whole number) between two values Example : I want to generate random numbers between 1 and 10: Formula := RANDBETWEEN (1,10)

Question 34

Trial

Answer 34

A single run through of an experiment. Example: a role of the dice

Question 35

Outcome Probability Random number matching

Answer 35

Tool Equation Number of trials Description

Question 36

Assumptions

Answer 36

Independent events are events that do not affect or are not affected by another event. Example: Each coin toss is not affected by the previous coin toss

Question 37

Assumptions

Answer 37

An event is dependent if one event occurring changes the probability of the other event occurring. Example: In a mixed bag of chocolates the probability of getting a blue chocolate changes each time someone takes a chocolate

Question 38

Assumption of eyecolour

Answer 38

According to genetics the eyecolour of the parents is critical in determining what eye colour the children can possibly have. Example: If both parents have blue eyes that is a recessive characteristic and the only possible eyecolour that their children can have it blue

Question 39

Assumptions that were not upheld

Answer 39

They were false

Question 40

Effect of the assumptions on the simulation

Answer 40

Assumptions affect the validity and reliability of our: -simulation -analysis and -conclusion

Question 41

Data

Answer 41

Generating simulation data for the model. Example : -Data recorded -Data processed -Draw graphs -Calculate probability or average

Question 42

Analysis/ Kaupapa

Answer 42

Analysing the model -center -Distribution -Shape

Question 43

center

Answer 43

Mean median mode

Question 44

Mode

Answer 44

Most frequent value

Question 45

Median

Answer 45

A value where 50% of the data lies above and below it

Question 46

Mean

Answer 46

Mean= sum of the data Over sample size

Question 47

Frequency

Answer 47

The number of times an event occurs

Question 48

Relative frequency

Answer 48

P(event)= frequency of outcome Over Total number of outcomes

Question 49

Conclusion

Answer 49

Applying the model to the real world problem. Example: -Answer questions -Random variation -Improvements -Limitations

Question 50

Random variation

Answer 50

Each time we run another simulation, we will generate different random numbers which will lead to different estimates of the probability and mean.