Probability Review - Stevens Institute of Technology
Probability Review Probability Probability = mathematic interpretation of uncertainty Uncertainty plays a major role in engineering decision making. Set = collection of: Items Events
Occurrences Distribution = behavior of a set Monte Carlo Method Statistic Analysis: Have a set Derive a distribution Monte Carlo Method:
Have a distribution Construct a model set Example 1 Deterministic calculation of deflection for a cantilever beam with quadratic cross section: Deflection = 4 F L3 / E W H3 L = length of beam W = width of beam
H = height of beam I = area moment of inertia E = Youngs modulus F = applied downward force Example 1 Stochastic Calculation: Deflection = 4FL^3/EWH^3 Symbols (physical parameters) represent distributions (expressed in MATLAB as vectors).
Vectors (distributions) should: have the same number of elements be randomly constructed according to preset rules regarding each quantity. Common Distributions Uniform: Constant probability over a range of values. Useful for round-off errors
Normal/Gaussian: Bell curve. Useful for large samples of random occurrences such as height. Common Distributions Gamma: Only defined for positive x Useful for time dependant events, arrivals, etc. Exponential:
A form of the Gamma, memoryless (events do not affect following occurrences) Weibull: A good representation of the frequency of failure for many types of equipment Deterministic v. Stochastic Results Programs
Matlab More than Matrices Useful tool for Monte Carlo Modeling Excel Used to process results of Matlab models Useful Commands in Matlab
R = unifrnd(A,B,m,n) generates uniform random numbers with parameters A and B, where scalars m and n are the row and column dimensions of R. R = normrnd(MU,SIGMA,m,n) generates normal random numbers with parameters MU and SIGMA, where scalars m and n are the row and column dimensions of R.
R = gamrnd(A,B,m,n) generates gamma random numbers with parameters A and B, where scalars m and n are the row and column dimensions of R. R = exprnd(MU,m,n) generates exponential random numbers with mean MU, where scalars m and n are the row and column dimensions of R. R = wblrnd(A,B,m,n) generates Weibull random numbers with parameters A and B, where scalars m and n are the row and column dimensions of R.
COM, DCOM and Software Components Nat Brown COM Program Management Microsoft Corporation [email protected] Agenda What are COM and DCOM? What's right with COM What's wrong with CORBA / IIOP Interesting COM Research Topics Additional Reference Material The COM Programming Model...
Explain why 'Jua Kali' workshops are very important in Kenya's Economy (6). Rules and regulations must be reduced in order for informal sectors to develop . Discuss this statement explaining reasons (4). What are the advantages and disadvantages of LEDC's...
To escape natural disasters: many Irish immigrants came to America in the 1800s to escape the famine that hit their country. This famine was followed by an epidemic of typhus. In search of religious freedom: Some people, such as Jews...
PENGANTAR PUBLIC RELATIONS RAHMA SANTHI ZINAIDA, M.I.Kom Chapter 1 - Tujuan PR Tujuan utama dari public relation adalah mempengaruhi perilaku orang secara individu maupun kelompok saat saling berhubungan, melalui dialog dengan semua golongan, dimana persepsi, sikap dan opininya penting terhadap...
After a thorough on-the-job training the reliever takes the responsibility for all the tasks on the farm Norske Landbrukstenester - ditt lokale vikarbyrå Persons over 16 years can be a reliever If employed, it is important that the reliever can...
I ship from my office, not the person's lab/office. I acquire packaging, unless they already have something suitable. I use FedEx. Bill shipping charges to lab, either by using their FedEx account number or billing back. So, how does this...
Relationships Among Numerical Variables. To study relationships among numerical variables, a new type of chart, called a scatterplot, and two new summary measures, correlation and covariance, are used. These measures can be applied to any variables that are displayed numerically.
Ready to download the document? Go ahead and hit continue!