Question1: Exhibit the use of continuous probability distribution and discrete probability distribution for quantitative risk management using examples.
Probability Distribution:
Continuous probability distributions are used extensively in modeling and simulations and represent the uncertainty in values such as tasks durations or cost of project components work packages. These distributions may help us perform quantitative analysis.
Discrete distributions can be used to represent uncertain events (an outcome of a test or possible scenario in a decision tree)
The most common numerical technique for PRA (analyses in which a large number of variables need to be evaluated simultaneously) in large scale air risk assessments is Monte Carlo simulation. Monte Carlo simulation integrates varying assumptions, usually about exposure, to come up with possible distributions (or ranges) of risk instead of point estimates. A continuous probability distribution can be displayed in a graph in the form of either probability density functions (PDFs) or corresponding cumulative distribution functions (CDFs).
A well-known example of a random variable is the number of points in a throw of a fair die. This number can be 1, 2, 3, 4, 5, or 6, and all six values are equally likely, i.e they all have the same probability, 1/6. If such a die is thrown a large number of times, this implies, for example, that a ‘6’ will occur in about one sixth of all throws.
Random variables are thus completely characterized by a so-called ‘probability distribution’. This specifies the occurrence probability for each value the variable can assume. In the case of continuous random variables, the corresponding probability distribution becomes a continuous function and...
... middle of paper ...
... people was given due weightage and it was multiplied with a seniority factor. I also incorporated minimum stay duration and results of a technical quiz. The cumulative factor was the divided by no of nights people have stayed abroad. This resulted in a merit figure which also ensured automatically that same people are not detailed again and again.
Lastly and most importantly, there was a lack of communication which needs to be addressed regarding this mechanism. So, I devised a dashboard and displayed it on assembly areas. This resulted in people getting acquainted with their turn. As the system was mathematical formula so there was no unfair biasedness which could creep in. Moreover, I gave one time open chance to everybody to come up and discuss anomalies if any. This resulted in motivation of people as well as conflict was resolved in a very rightful manner.
(Total the number of observations. Summarise the observations (risk and prioritise them in a list due to the final figures )
Introduction to the basic concepts of probability and statistics with discussion of applications to computer science.
...vent occurs k times per unit of measurement”. The Poisson distribution is a frequently used formula in works by Xenakis.
(i) P(0 ≤ Z ≤ 1.3) (ii) P(−1.3 ≤ Z ≤ 0) (iii) Area to the right of Z = 1.6 (iv) Area to the left of Z = 1.4 (v) P(−1.7 ≤ Z ≤ 2.7) (vi) P(−1.7 ≤ Z ≤ − 0.7) (vii) P(1.7 ≤ Z ≤ 2.7)
Many theories of logic use mathematical terms to show how premises lead to conclusions. The Bayesian confirmation theory relates directly to probability. When applying this theory, a logician must know the probability of a given situation, have a conditional rule, and then he or she must apply the probability when the conditional rule is applied. This theory is used to determine an outcome based on a given condition. The probability of a given situation is x, when y occurs, or the probability is z if it does not occur. If y occurs, then the outcome of the given would be x. For example, if there is a high probability that a storm will occur if a given temperature drops and there is no temperature change, then it will most likely not rain because the temperature did not change (Strevens, 2012). By using observational data such as weather patterns, a person can arrive at a logical prediction or conclusion that will most likely come true based...
After hours of independently researching the field of Actuarial Science, I contacted Mr. Michael Miller. Mr. Miller is the Director of Insurance Pricing at Catlin Inc., a private insurance company in Atlanta, Georgia. With a Masters of Science in Mathematics and classification as a Fellow of Casualty Actuarial Society, Mr. Miller has thrived in the field of Actuarial Science for twenty years. He has even achieved the position of President of the Casualty Actuarial Society of the Southeast.
Statistics work for everything when there is a lot of it. They work for money, molecules, atoms, star systems, and even people. People tend to adhere to statistics when there is a fair amount of people to stifle the occasional fluctuations in human behavior. Many things we do depend on statistics. Take war for example. War is a very good example, since the outcome depends more on the general strategy of the whole war, than on individual soldiers. It follows definite rules that can be expressed in formulas. The individual people in war tend to become statistics, in the eyes of the high command, the public, as well as in their own perception. Tim O’Brien wonderfully illustrates this in his essay “How to Tell a True War Story.” He relates that there is no point to any events or actions according to the perception of the soldier during a war. “You smile and think, ... what’s the point?” (469) he says. A person then becomes nothing more than a statistic -- a part of a whole behaving in a random way. If there is no point to existence, then his actions are truly random. Something truly random can be easily studied, stimulated, expressed in some numbers, percentages, probabilities. This randomness of the soldier is what the whole military apparatus depends on. Consider: if the life of a soldier during war had a point, if he realized that there is some underlying meaning, wouldn’t he strive toward the goal assigned by that meaning? He would, for that is in human nature. Now, if there was no meaning in his perception, he could easily be persuaded that a particular thing must be done. He will obediently follow.
Probability is always surrounding us from stock markets to the ever-simple heads or tails. This very complicated area of mathematics can be explained in a simpler way. It is how likely an event is to happen. The probability of an event will always be between 0 and 1. The closer it is to one, the more likely the event is to happen.
Finally, you develop an online survey to gather the predictive information from applicants. Then each candidate's biodata survey and resumes are screened electronically and given a score between zero and 100 based on how many of the top performance indicators each candidate possesses.
GM uses this system by containment, disposition, separation, and classification. Such a system guarantees that any outcome that does not comply with specified requirements is restricted from unintended use, restrained, and dispositioned by the administrators. Accompanied by this quality control is the verifying position where first-time quality and process capacity is advanced (Drew, 2011). Every team member is informed about any modifications in the production process and who and when to summon for assistance in the event of any quandary. Every team is also included in the problem solving to reach any improvement in goals.
The field of medicine is another high subscriber to this forecasting technique. Potential diagnoses are frequently made based on a patient’s history or that of his ancestors and the calculated likelihood of him/her acquiring certain conditions. Statistics and probability aid in the decision making process of which test may be required for a given symptom and how a possible outbreak may be detected and contained. Strategies for isolating and dealing with diseases are often made with the aid of statistics on the percentage of a population that may have been infected and the probability of its escalation.
Because they occur so frequently, there is an infelicitous propensity to invoke mundane distributions in situations where they may not be applicable. As Lippmann verbally expressed, "Everybody believes in the exponential law of errors: the experimenters, because they cerebrate it can be proved by mathematics; and the mathematicians, because they believe it has been established by observation"
Another important aspect in towards positive group dynamics is to make all members feel accepted in spite of any diversity. Trust is an important trait for the survival of a group. More importantly, the likelihood of accomplishing goals increases with maximum trust and confidence. However, numerous personalities with different backgrounds may cause friction while attempting to resolve conflicts or reaching a consensus. These challenging situations can lead to stress and tension amongst the group members, but when successfully resolved they lead to further strengthening of the bonds and the emergence of a more cohesive group. Also certain measures can be taken to avoid certain petty discrepancies right from the beginning. Specific ground rules; code of ethics and conduct should be established that would encourage smooth functioning and efficient target
After identifying the risk, next step is to decide how to handle those risk. There are four main strategies that can help to decide what to do with the
Pascal’s Triangle, because it contains binomial coefficients, is also a representation of the binomial distribution that includes all probability values for finite numbers of experiments with two possible outcomes. Pascal’s Pyramid, then, should represent both the numerical coefficients of the expansion of a trinomial raised to a power and the values in a trinomial expansion.