Question

2020-11-08

Stochastic modeling is a form of financial model that is used to help make investment decisions. This type of modeling forecasts the probability of various outcomes under different conditions, using random variables.
Stochastic modeling presents data and predicts outcomes that account for certain levels of unpredictability or randomness. Companies in many industries can employ stochastic modeling to improve their business practices and increase profitability. In the financial services sector, planners, analysts, and portfolio managers use stochastic modeling to manage their assets and liabilities and optimize their portfolios.
Deterministic modeling produces constant results
Deterministic modeling gives you the same exact results for a particular set of inputs, no matter how many times you re-calculate the model. Here, the mathematical properties are known. None of them is random, and there is only one set of specific values and only one answer or solution to a problem. With a deterministic model, the uncertain factors are external to the model.
Stochastic modeling produces changeable results
Stochastic modeling, on the other hand, is inherently random, and the uncertain factors are built into the model. The model produces many answers, estimations, and outcomes—like adding variables to a complex math problem—to see their different effects on the solution. The same process is then repeated many times under various scenarios.
Stochastic modeling is used in a variety of industries around the world. The insurance industry, for example, relies heavily on stochastic modeling to predict how company balance sheets will look at a given point in the future. Other sectors, industries, and disciplines that depend on stochastic modeling include stock investing, statistics, linguistics, biology, and quantum physics.
A stochastic model incorporates random variables to produce many different outcomes under diverse conditions.

asked 2021-03-09

Define the term Mean.

asked 2021-02-04

In these problem you are asked to find a function that models a real-life situation. Use the principles of modeling described in this Focus to help you. Radius find a function that models the radius r of a circle in term of its area A.

asked 2021-01-23

asked 2021-03-07

This problem is about the equation

dP/dt = kP-H , P(0) = Po,

where k > 0 and H > 0 are constants.

If H = 0, you have dP/dt = kP , which models expontialgrowth. Think of H as a harvesting term, tending to reducethe rate of growth; then there ought to be a value of H big enoughto prevent exponential growth.

Problem: find acondition on H, involving \(\displaystyle{P}_{{0}}\) and k, that will prevent solutions from growing exponentially.

dP/dt = kP-H , P(0) = Po,

where k > 0 and H > 0 are constants.

If H = 0, you have dP/dt = kP , which models expontialgrowth. Think of H as a harvesting term, tending to reducethe rate of growth; then there ought to be a value of H big enoughto prevent exponential growth.

Problem: find acondition on H, involving \(\displaystyle{P}_{{0}}\) and k, that will prevent solutions from growing exponentially.

asked 2020-11-26

Two drugs, Abraxane and Taxol, are both cancer treatments, yet have differing rates at which they leave a patient’s system. Using terminology from pharmacology, Abraxane leaves the system by so-called “first-order elimination”, which means that the concentration decreases at a constant percentage rate for each unit of time that passes. Taxol leaves the system by “zero-order elimination”, which means that the concentration decreases by a constant amount for each unit of time that passes.

(a) As soon as the infusion of Taxol is completed, the drug concentration in a patient’s blood is 1000 nanograms per milliliter \(\displaystyle{\left(\frac{{{n}{g}}}{{{m}{l}}}\right)}.\) 12 hours later there is \(\displaystyle{50}\frac{{{n}{g}}}{{{m}{l}}}\) left in the patient’s system. Use the data to construct an appropriate formula modeling the blood concentration of Taxol as a function of time after the infusion is completed.

(b) As soon as the infusion of Abraxane is completed, the drug concentration in a patient’s blood is 1000 nanograms per milliliter \(\displaystyle{\left(\frac{{{n}{g}}}{{{m}{l}}}\right)}\). 24 hours later there is \(\displaystyle{50}\frac{{{n}{g}}}{{{m}{l}}}\) left in the patient’s system. Use the data to construct an appropriate formula modeling the blood concentration of Abraxane as a function of time after the infusion is completed.

(c) Find the long-term behavior of the function from part (b). Is this behavior meaningful in the context of the model?

(a) As soon as the infusion of Taxol is completed, the drug concentration in a patient’s blood is 1000 nanograms per milliliter \(\displaystyle{\left(\frac{{{n}{g}}}{{{m}{l}}}\right)}.\) 12 hours later there is \(\displaystyle{50}\frac{{{n}{g}}}{{{m}{l}}}\) left in the patient’s system. Use the data to construct an appropriate formula modeling the blood concentration of Taxol as a function of time after the infusion is completed.

(b) As soon as the infusion of Abraxane is completed, the drug concentration in a patient’s blood is 1000 nanograms per milliliter \(\displaystyle{\left(\frac{{{n}{g}}}{{{m}{l}}}\right)}\). 24 hours later there is \(\displaystyle{50}\frac{{{n}{g}}}{{{m}{l}}}\) left in the patient’s system. Use the data to construct an appropriate formula modeling the blood concentration of Abraxane as a function of time after the infusion is completed.

(c) Find the long-term behavior of the function from part (b). Is this behavior meaningful in the context of the model?

asked 2020-11-09

Define CASE terms and concepts, including a
repository, modeling tools, documentation tools,
engineering tools, and construction tools

asked 2021-01-16

To find: The function that models the area of rectangle in terms of length of one of its sides.
The perimeter of rectangle is 20 ft.

asked 2020-11-29

In these problem you are asked to find a function that models a real-life situation.

Area. Find a function that models the surface area S of a cube in terms of its volume V.

Area. Find a function that models the surface area S of a cube in terms of its volume V.

asked 2021-02-09

The admissions office of a college wants to determine whether there is a relationship between IQ scores x and grade-point averages y after the first year of school. An equation that models the data obtained by the admissions office is

\(\displaystyle{y}={0.069}{x}-{4.755}.\)

Estimate the values of x that predict a grade-point average of at least 3.5. (Simplify your answer completely. Round your answer to the nearest whole number.)

\(\displaystyle{y}={0.069}{x}-{4.755}.\)

Estimate the values of x that predict a grade-point average of at least 3.5. (Simplify your answer completely. Round your answer to the nearest whole number.)

asked 2021-01-23

Modeling \(\displaystyle{C}{O}_{{2}}\) emissions

a) Use the data from 1960 and 1990 to find a linear function that models the \(\displaystyle{C}{O}_{{2}}\)

b) Use your linear function to predict the \(\displaystyle{C}{O}_{{2}}\) emissions in 2005. Compare your prediction with the actual \(\displaystyle{C}{O}_{{2}}\) emission in 2005

a) Use the data from 1960 and 1990 to find a linear function that models the \(\displaystyle{C}{O}_{{2}}\)

b) Use your linear function to predict the \(\displaystyle{C}{O}_{{2}}\) emissions in 2005. Compare your prediction with the actual \(\displaystyle{C}{O}_{{2}}\) emission in 2005