1. Probability Refresher COMP5416 Advanced Network Technologies

2. School of Information Technologies COMP5416 Simulation - 2 Discrete random variables Events can take only discrete values, e.g. integer values 123456value Probability Probabilities sum to 1.0

3. School of Information Technologies COMP5416 Simulation - 3 Example – Roll a die Discrete values 1,2,3,4,5,6 Each with probability 1/6

4. School of Information Technologies COMP5416 Simulation - 4 Example – Bernoulli random variable Discrete values 1 with probability p, 0 with probability 1- p 01value Probability p 1-p

5. School of Information Technologies COMP5416 Simulation - 5 Example – Poisson random variable Discrete values 0,1,2,...,infinity Value k has probability p k, with 123456value Probability 07

6. School of Information Technologies COMP5416 Simulation - 6 Continuous random variables Events can take real values on arbitrary range Probabilities integrate to 1.0

7. School of Information Technologies COMP5416 Simulation - 7 Continuous random variables Distribution Function

8. School of Information Technologies COMP5416 Simulation - 8 Example – negative exponential random variable Parameter  Probability density function, negative exponential,  =2 Probability distribution function, negative exponential,  =2

9. School of Information Technologies COMP5416 Simulation - 9 Example – Gaussian random variable Parameters  Gaussian density function,  =0,  =1 Gaussian distribution function,  =0,  =1