lOMoARcPSD|37763557
Module 1 – Expected Value
Model: high-level representations of the operation of a real-world process or system (discrete vs. continuous, stochastic vs. deterministic (no
randomness), dynamic vs. static)
Solving a model: 1) Analytical: model using physical/ mathematical equations, 2) Numerical: Model weather (too tough for exact analytical models), and
3) Simulation model: To add randomness
Advantages of simulation: Disadvantages:
Can study models too complicated for analytical / numerical treatment Sometimes not so easy.
Study detailed relations that might be lost in the analytical or numerical treatment Sometimes very time consuming / costly.
Use as a basis for experimental studies of systems. Simulations give “random” output (and lots
Use to check results and give credibility to conclusions obtained by other methods of misinterpretation of results is possible).
Reduce design blunders To do a certain problem, better methods
Really nice demo method than simulation may exist.
(Sometimes) very easy.
Moment Generating Function
Module 2 - Calculus, Probability, and Statistics Review
Finding Zeroes
Method for complicated non-linear function: Trial/error,
bisection, Newton’s method & fixed-point method
Functions of Random Variable
Integration
Jointly Distributed Random Variables
Integration Computer Exercise
L’Hospital’s Rule
Conditional Expection & Double expection won’t be on test
Probability
Covariance and Correlation
Simulating RV
Finding pdf of a function knowing pdf of other function
cheatsheet
Probability Distributions
Discrete Y = number of success
Limit Theorem
How many Bernoulli trials to take until the rth success occurs
Introduction to Estimation
Continuous
This study source was downloaded by 100000899606070 from CourseHero.com on 02-22-2026 22:25:04 GMT -06:00
Downloaded by Alice Hu ()
https://www.coursehero.com/file/244572031/ISYE-6644-Midterm-1-Cheat-Sheetpdf/
Module 1 – Expected Value
Model: high-level representations of the operation of a real-world process or system (discrete vs. continuous, stochastic vs. deterministic (no
randomness), dynamic vs. static)
Solving a model: 1) Analytical: model using physical/ mathematical equations, 2) Numerical: Model weather (too tough for exact analytical models), and
3) Simulation model: To add randomness
Advantages of simulation: Disadvantages:
Can study models too complicated for analytical / numerical treatment Sometimes not so easy.
Study detailed relations that might be lost in the analytical or numerical treatment Sometimes very time consuming / costly.
Use as a basis for experimental studies of systems. Simulations give “random” output (and lots
Use to check results and give credibility to conclusions obtained by other methods of misinterpretation of results is possible).
Reduce design blunders To do a certain problem, better methods
Really nice demo method than simulation may exist.
(Sometimes) very easy.
Moment Generating Function
Module 2 - Calculus, Probability, and Statistics Review
Finding Zeroes
Method for complicated non-linear function: Trial/error,
bisection, Newton’s method & fixed-point method
Functions of Random Variable
Integration
Jointly Distributed Random Variables
Integration Computer Exercise
L’Hospital’s Rule
Conditional Expection & Double expection won’t be on test
Probability
Covariance and Correlation
Simulating RV
Finding pdf of a function knowing pdf of other function
cheatsheet
Probability Distributions
Discrete Y = number of success
Limit Theorem
How many Bernoulli trials to take until the rth success occurs
Introduction to Estimation
Continuous
This study source was downloaded by 100000899606070 from CourseHero.com on 02-22-2026 22:25:04 GMT -06:00
Downloaded by Alice Hu ()
https://www.coursehero.com/file/244572031/ISYE-6644-Midterm-1-Cheat-Sheetpdf/
