1. Discrete Multivariate Distributions Revision and Simulation
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ST2352 Week 2

2. Simulation
Excel file
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ST2352 Week 2

3. Bivariate Dist (Marg) Dist X Cov(X,Y) Dist (X+Y) Var(X+Y) E[min(X,Y)]
Derive by probability
Explain by simulation
Marginalise:
Prob: sum across one dim
Sim: ignore one col
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ST2352 Week 2

4. Summaries of sample
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ST2352 Week 2

5. Multivariate Stochastic System
Multiple Columns/Random Variables
Interest often lies in a few cols/RVs
Marginalise
ST2351. Tut2.Q2
Sit 6 exams.
Pr pass each is 0.8
indep others
Pr(Fail at least 2)=
18/01/2019
ST2352 Week 2

6. Conditional Distribution
Simulating from Cond distribution
Simulate system
And restrict attention to subset (of random size)
Alt
Focus on aspect of joint sim (rescale rel freq) |
18/01/2019
ST2352 Week 2

7. Conditional Distribution
Simulating from Cond distribution
Compute by prob
Explain by simulation
Dist [X|Y=0]
E [X |Y=0]
Var[X|Y=0]
E [X2 |Y=0] |
Prove. Explain via simulation
18/01/2019
ST2352 Week 2

8. Conditioning in Stoch Systems
Modelling uncertainties in system
Exploiting partial info on a system
X and Z often multivariate in real applications
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ST2352 Week 2

9. Stoch System: Exams Passed
Pr(Pass exam A, B, C, D):
A B C D 0.9
Seek dist of N = no. exams past
Simulation and Marginalising
Probability
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ST2352 Week 2

10. Prob method 1: Enumeration
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ST2352 Week 2

11. Prob method 2: Recursion via Conditional Dist
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ST2352 Week 2

12. Prob method 2: Recursion via Conditional Dist
18/01/2019
ST2352 Week 2