Modeling data distributions #2 - Questions and Answers

Question 1 Define the term stochastic models? Answer 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. Question 2 What is a data model, and why is its purpose? What is conceptual modeling? What do we need to use conceptual modeling? What are the functions of a DBMS? Provide an example of their use. Answer Step 1 Data model: Data modeling is a technique used to define and organize your business processes. It allows you to create a visual description of your business by examining, understanding, and clarifying your data requirements and how they underpin your business. It provides a clear picture of the base data and can be used by database developers to create a physical database. Conceptual modeling: A conceptual model is a description of a system, made of the composition of notions that are used to help people identify, understand, or simulate a subject the model represents. The three basic tenants of the Conceptual Data Model are Entity: A real-world thing Attribute: Characteristics or properties of an entity Relationship: Dependency or association between two entities Uses of Conceptual modeling: A conceptual models Question 3 Let's say the widget maker has developed the following table that shows the highest dollar price p. widget where you can sell N widgets. Number N Price p 20053.00 25052.50 30052.00 35051.50 (a) Find a formula for pin terms of N modeling the data in the table. (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in month as a function of the number N of widgets produced in a month. R Is Ra linear function of N? (c) On the basis of the tables in this exercise and using cost, C = 35N + 900, use a formula to express the monthly profit P, in dollars, of this manufacturer asa function of the number of widgets produced in a month p = ? Answer As per bartleby guidelines for the more than 3 subparts only first three are to be answered please upload the others separately. (a) Consider the two points from table (a) as (200 53.00) and (250 52.50). Then, the equation is, p = P₁ = (P2-P1) (N N2-N1 p-53.00 = (52.50-53.00) (N-200) 250-200 p-53 = -0.50 (N-200) P 53 -0.01N + 2 N1) p = -0.01N + 55 Thus, the equation p = -0.01N +55. (b) Consider the formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month. R = (-0.01N +55)N = -0.01N2 + 55N Thus, the formula is R = -0.01N2 + 55N. Here, R is not the linear function of N. (c) The formula for the monthly profit is, P = -0.01N2 + 55N - 35N - 900 = -0.01N2 + 20N-900 Here, P is not the linear function of N. Question 4 Regarding z-scores: a. How is a z-score obtained? b. What is the interpretation of a z- score? c. An observation has a z-score of 2.9. Roughly speaking, what is the relative standing of the observation? Answer The Z-score evaluates how closely a given value relates to the mean of a set of values. It provides the specific data point's standard deviation from the mean. The general formula Z = x - population mean population standard deviation b. Case 1: If a data point has a Z-score of -3, this indicates that the data point is 3 standard deviations away from the mean. Case 2: If a data point has a Z-score of 0, it means that the data point is 0 standard deviations away from the mean. The data point is therefore equal to the mean. Case 3: If a data point has a Z-score of 3, this indicates that the data point is 3 standard deviations above the mean. c. Because over 95% of values in normal distributions fall within two standard deviations, the observation is relatively high. Question 5 MODELING REAL LIFE. To make 18 glasses of juice, combine 0.25 cups of juice concentrate with 2 cups of water. Use how much juice concentrate? How much water do you use? You use cups of juice concentrate and Answer Step 1 cups of water. According to the information provided, 0.25 cups of juice are mixed into every 2 cups of water. 0.25 cups 1 cups 2 cups 8 1 So, each cup of juice has cups of juice concentration. Step 2 Obtain enough juice to fill 18 cups. 18x()=18 9 4 = 2.25 cups of juice concentration 182.25 15.75 cups of water So, you use 2.25 cups of juice concentration and 15.75 cups of water.