Probability Distributions:
Uniform: each result has same probability (rolling a single dice)
Normal: z is the number of stan dev’s away from the mean = z = value – mean / st dev.
Binomial: (put formula here)
Triangular: has mode (most likely), max and min.
Poisson: a discrete distribution (a count) number of successes in an interval (λ) depends on the success rate and the interval length.
Exponential: μ is average time to complete a task, or interval between events. It is a continuous distribution. If poisson rate applies, then interval between is exponential.

Above formula will give you percentage that the task will be completed within x mins of the average.Turn the interval (μ) into a rate (λ) λ = 1/μ – f(x) = λe- λx

Simulation is the process of designing a mathematical or logical model of a real system and then conducting computer-based experiments with the model to describe, explain, and predict the behavior of the real system.
Simulation is the most widely used Decision Analysis technique used to gain knowledge about outcomes to assess risk
Continuous Simulation: based on math eqn’s and used for simulating continuous values. (time spend waiting in line) s 1 s 2 s 3 d 1
0
0
9,000
9,000 d 2
2,000
500
4,000
4,000 d 3
5,000
1,500
0
5,000
Maximum
Regret
Decision
Regret
Table
States of Nature
Discrete Simulation: simulation specific values or points (number waiting in queue)
Advan: leads to better understanding, can model any assumptions, easier to explain, provides a more realistic replication.
Disadvan: no guarantee it will provide good results, no way to prove reliable, time consuming, it’s random based may be less accurate.

The Monte Carlo technique is defined as a technique for selecting numbers randomly from a probability distribution for use in a trial (computer run) of a simulation model.

Validation and Verification
Verification done by expert, validation can be done by using past data in simulation and seeing if results are correct.
Steps in Validation: 1. develop model that looks reasonable to those that understand system 2. Validate assumption 3. Validate output
You are looking for the long run steady state operation of a system

QUEUING
Size of population can be infinite or finite
Behaviour of arrivals (patient, balk, renege)
Waiting line can have limited or unlimited capacity

DECISIONS WITH UNCERTAINTY
Laplace (assume equally likely) MAXIMAX (MAX the MAXimum Payoff) Take the Maximum value from all the maxs

MAXIMIN (MAX the Minimum Payoff) Take the greatest value from all the mins

MINIMAX Regret (minimize Opport Cost) Take the oppourtunity loss of each cell, and take the decision which has the least highest regret.

These are for PROFIT, the opposite are for