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some descriptive questions on statistics

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Our study group have various prospectives about the following questions. Please help us by answering based on your expertise. Many thanks.

1. Describe the use of sensitivity analysis and postoptimality analysis in analyzing the results.

2. Describe the characteristics of a Bernoulli process. How is a Bernoulli process associated with the binomial distribution?

3. What is the purpose of decision trees? How are they constructed?

4. What is the overall purpose of utility theory? Explain using an example.

5. Explain simple linear regression. What are the potential pitfalls of regression analysis?

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https://brainmass.com/statistics/regression-analysis/sensitivity-analysis-bernoulli-process-decision-trees-129720

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Sensitivity Analysis/Bernoulli Process/Decision Trees

1. Describe the use of sensitivity analysis and post optimality analysis in analyzing the results.
An LP model is always solved using some deterministic assumptions. We assume that coefficients of all the variables are known with certainty. In real world, the situations are generally dynamic, thus this type of certainty rarely exists.

To see the effect of changes in the situations after an optimal solution has been found for an LPP, a process called 'Post optimality analysis' or 'Sensitivity Analysis' is used.
Sensitivity analysis helps answer questions about how sensitive the optimal solution is to changes in various coefficients in a model.
With sensitivity analysis, effect of following type of changes on a current optimal solution can be assessed:
• Change in objective function coefficients
• Change in RHS values of constraints
• Change in constraint coefficients
• Effect of addition of a new variable in the current problem
Various packages used to solve the LP Problems like Excel Solver, LINDO, LINGO, QM etc generate sensitivity analysis report along with the optimal solution. Using this report, a series of What-if questions can be answered about the LP Model in consideration.

One example of the use of sensitivity analysis could be in a simple product mix problem where there is certain amount of resources available with each product needing some amount of each resource. The problem may be that of finding a product mix that would maximize the total profit.

Once the problem is solved using LPP, the next question could be like:" what happens if resource 1 is increased by a certain amount?" or "what happens if the profit margin of product 1 changes to say $10 from $8"?
These questions can be easily answered using the Sensitivity report generated along with the ...

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