Download Examination Questions Stochastic Modeling in Industry (SMI) The

Examination Questions
Stochastic Modeling in Industry (SMI)
The magistrates, Course 1, English, Second half-year, 2016 – 2017 academic year, 3 credits
1. Elementary Probability Theory. Probability. Examples. Definition and illustrations.
2. Deductions from the axioms. Independent events. Arithmetical density. Examples. Exercises.
3. Random Variables. Examples. Definition of Random Variables.
4. Distribution and Expectation. Definition of Mathematical Expectation. Examples.
5. Integer-valued random variables. Examples.
6. Random variables with densities. General case. Exercises.
7. Distributions. Equiprobability distribution, Even/uniform distribution.
8. Binomial, Poisson distributions.
9. Geometric, Cauchy distributions.
10. Conditional, Conjugate, Dirichlet distributions.
11. Discrete, Exponential, Generalized inverse normal distributions.
12. Generalized inverse Gaussian distribution.
13. Isotropic vector in 3D space.
14. Methods of simulations of random variables. Pseudo-Random Number Generator.
15. Uniform Random Variable on the interval 0, 1 . Uniform Simulation. Algorithm a Uniform
Pseudo-Random Number Generation.
16. The Inverse Transform. Optimal Algorithms. General Transformation Methods. AcceptReject Methods.
17. The Fundamental Theorem of Simulation. The Accept-Reject Algorithm. Problems.
18. Random Walks. Markov Chains. Transition probabilities. Basic structure of Markov chains.
19. Stochastic Process. Random Walks.
20. Markov Chains. Computer simulation of Markov Chains.
21. Others Stochastic Process. Computer simulation of Markov Chains.
22. Linear and Nonlinear Stochastic Process.
23. Approximation and Computer simulation some Linear and Nonlinear Stochastic Processes
by Markov Chains.
24. Queue System Modeling. Algorithm of calculations. Quality of product calculations.
25. The Ruin of Gambler Problem.
26. Markov Chains in Economics. Howard model.
27. Computer simulation of the Poisson distribution (Poisson flow) and others random
parameters.
28. Calculations of probabilistic characteristics of product.
29. Calculations of neutron passing through of plate. Problem statement. Breakdown of
calculation by modeling of real trajectories.
30. Reactor calculation and protection.
31. Construction and Analysis of Empirical Models.
32. Estimation when Dependent Error of Measuring’s.
33. Correlated remains. Durbin – Watson Criterion of Serial Correlation. Example.
34. Strategics of Effective Experimentation. Canonical Analysis for Plastic Extruder. Example.
35. Linear Models with one variable.
36. Strategics of Effective Experimentation.
37. Bernoulli Binomial Distribution and their Applications.
38. Poisson Distribution and their Applications.
39. Technical characteristics of materials.
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Estimation Methods. Significance Test.
Estimation of Parameters.
Statistics Distribution. Criterion of Independence and Fitting Criterion.
Estimation of Mean and Variance.
Estimated of Correlation Coefficient.
Variance Analysis.
Sequential Analysis. Criterion for Randomness.
Correlation.
Variance Analysis.
Covariance Analysis.
Variance Analysis. One-Way Classification. Example.
Two-Way Classification. Example.
Covariance Analysis. Example.
Professor
Kanat Shakenov
April 1, 2017 y.
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