Random variable

Decision Variables O.F. – Objective Funtion S.T. or CONST - Constraints Constrained Mathematical Model – a model with an objective and one or more constraints EXAMPLE: 50D + 30C + 6M is the total profit for a production run($50 profit for Desk, $30 profit for Chair and $6 per pound for steel) Functional Constraints - ≤ ≥ or = --Restrictions that involve expressions with 1 or more variables EXAMPLE: 7d+3c+1.5M <= 2000 (constraint on raw steel) Variable Constraints – Involve only 1 variable – Nonnegativity

be done by generating random numbers from given probability distributions. The different steps of this simulation and assumption made are explained below. 1. Simulation for the repair time. It is given that the repair time follows Repair Time (days) Probability 1. .20 2. .45 3. .25 4. .10 ----- 1.00 To generate a random number from the above

Queuing Theory: Queuing theory is described as the study of waiting lines (Render et al, 2015). Believe it or not it is a theory we use daily. Some instances you may encounter applying this theory, could be when deciding on which line to wait on when making a purchase or when initiating a phone call for service to be placed on hold. Sometimes when being placed on hold in queue the company, for example Comcast, may tell that you are the fifth person on hold or in queue; they may even give you

information tutor: Expected value is the main thought in probability, in an intellect more general than probability itself. The expected value of a real-valued selection variable offers a compute of the center of the distribution of the variable. More considerably, by taking the expected value of various functions of a common random variable, we can calculate a lot of interesting features of its distribution, including spread and correlation. Tutor is a personality working in the education of others, either

Abstract Abstract here Humans, and animals, often perceive events as being random. Many lab oratory and controlled studies have been conducted over the last half-century to determine human ability to detect whether a particular string of events is random. Often, these studies consist of detecting whether some binary sequence has the properties of a bernoulli random variable. From the re sults of these studies, we can conclude experimental subjects hold the Law of Small Numbers (Tversky & Kahneman

to observe the random numbers, which is chosen in such a way that they directly simulate the physical random processes of the original problem, and to assume the preferred solution from the behavior of these random numbers. Monte Carlo simulation has wide application in performing risk analysis by building models of possible results by substituting a probability distribution for any factor that has inherent uncertainty. It then calculates results by using a different set of random values over and

each period under the different operating condition, which can be expressed as a random variable, the study system can be formulated through a MSP approach. Thus, in a MSP model for carbon emission management system, the objective is to maximize system benefits while satisfying the total carbon emission requirement. Specifically, the economic objective can be formulated as follows: （1a） where are decision variables that are reflected in the objective function and determined by the capacity of

INTRODUCTION: Identifying, defining risks (market risks as well as non-market risks), presenting and justifying a unified framework for the analysis, construction and implementation of risk measures are important components of insurance pricing. According to the Oxford’s advanced learners dictionary, risk can be defined as the possibility that something uncertain (not predictable) and unpleasant will happen. Both financial and insurance organisations are therefore faced with this concept of risk

the first win would help him regain from the previous losses plus win profit equal to the original stake [2]. If X1, X2,…, is a sequence of independent and identically distributed random variables with P(Xn = 1) = 1/2 , P(Xn = -1)= ½. Filtration (F_n )_n Fn = σ(X1,…,Xn). Then sequence (s_n )_(n=1)^∞(simple random variable walk on Z) is martingale w.t.r. (F_n )_n as E(Sn | Fn-1) = E(Sn-1 + Xn | Fn-1) = Sn-1 + E(Xn | Fn-1) = Sn-1 + E(Xn) = Sn-1 [1] Poyla’s Urn – A container has balls of two color, say

using a different set of random values from the probability functions. The simulation could involve tens and thousands of recalculations before its