L8 - Simulation - Random Digits

Question 1

How do you sample from a Discrete distribution?

Answer 1

Assuming that we have a table of outcomes and associated probabilities (expressed as percentages):
1. Add a column to the table containing cumulative percentage
2. Add a further column to the table entitled Random Digits
3. In the row corresponding to the first outcome, begin with “00” and go up to one less than the
cumulative percentage for that row
4. In subsequent rows, begin with the next pair of digits following on from the previous row and go
up to one less than the cumulative percentage for that row – so the final row will end with “99”
5. Take a pair of uniformly distributed random digits (i.e. digits in the range 00–99) and then choose
the outcome corresponding to where these digits are located in the Random Digits column

Question 2

Why is using more decimal places for probabilities not a good idea?

Answer 2

• in practice historical data is often used to estimate the percentage, which will be subject ot the inaccuracies and variability associated with samples

Question 3

How do you sample from Continuous Uniform Distribution?

Answer 3

• Equally likely to be between min and max
  𝑋=”min”+(“digits” /100×(“max” −”min” ))
• If digits=“00”, then X = min
• If digits=“99”, then X = max (nearly)

Question 4

How do you sample from a Histogram?

Answer 4

• Use discrete to determine category (which bar), i.e. approriate min/max
  Use uniform to model actual value

Question 5

How do you sample from a normal distribution?

Answer 5

1. Take pair of random digits
2. Divide random digits by 100 to obtain probability
3. Find probability in Prob column, look across to find Z
4. Use formula below to convert Z value:
   X=𝜇+𝜎𝑍
   Where μ is the mean and σ is the standard deviation and X is the simulated value of interest

TAKE Z VALUE TABLE INTO EXAM

Question 6

How do you sample from a negative Exponential Distribution?

Answer 6

Take pair of random digits
2. Divide random digits by 100 to obtain probability
3. Find probability in Prob column, look across to find Z
4. Use formula below to 1. convert Z value
𝑋=𝜇𝑍
Where μ is the mean and X is the simulated value of interest
- USE SPECIFIC Z TABLE (NOT NORMAL DISTRIBUTION ONE)

Question 7

Why use Process ‘Maps’?

Answer 7

by drawing each stage that needs to be modelled separately, it might give you a better overall picture of what needs to be done

Question 8

LAST PART OF L8

Answer 8

START OF L9