Quiz#1 Review Sheet - Question & Answer - Quiz, Flashcards & Trivia

1. How can PI be calculated using Monte Carlo method?

By simply multiplying the diameter of a circle by a constant value to get an accurate estimate of PI.

By drawing a square and circle, and then randomly choosing coordinates within the square to calculate the value of PI.

By conducting a series of mathematical equations involving the square root and sine functions to estimate the value of PI.

Note: (from the BasicsOfMonteCarloSimulations.doc)
"Hit and miss"integration is the simplest type of MC method to understand, and it is the typeof experiment used in this lab to determine the HCl/DCl energy level populationdistribution. Before discussing the lab, however, we will begin with a simplegeometric MC experiment which calculates the value of pi based on a "hitand miss" integration.Monte Carlo Calculation of Pi
If we say our circle'sradius is 1.0, for each throw we can generate two random numbers, an x anda y coordinate, which we can then use to calculate thedistance from the origin (0,0) using the Pythagorean theorem. If the distancefrom the origin is less than or equal to 1.0, it is within the shaded area andcounts as a hit. Do this thousands (or millions) of times, and you will wind upwith an estimate of the value of pi. How good it is depends on how manyiterations (throws) are done, and to a lesser extent on the quality of therandom number generator. Simple computer code for a single iteration, or throw,might be: x=(random#) y=(random#) dist=sqrt(x^2 + y^2) if dist.from.origin(less.than.or.equal.to) 1.0 lethits=hits+1.0

Wiki Source: (Using Monte Carlo Method)

For example, consider a circle inscribed in a square. Given that the circle and the square have a ratio of areas that is ?/4, the value of ? can be approximated using a Monte Carlo method: (4 STEPS BELOW)
1) Draw a square on the ground, then inscribe a circle within it.2) Uniformly scatter some objects of uniform size (grains of rice or sand) over the square.3) Count the number of objects inside the circle and the total number of objects.4) The ratio of the two counts is an estimate of the ratio of the two areas, which is ?/4. Multiply the result by 4 to estimate ?.
In this procedure the domain of inputs is the square that circumscribes our circle. We generate random inputs by scattering grains over the square then perform a computation on each input (test whether it falls within the circle). Finally, we aggregate the results to obtain our final result, the approximation of ?.
To get an accurate approximation for ? this procedure should have two other common properties of Monte Carlo methods.

First, the inputs should truly be random. If grains are purposefully dropped into only the center of the circle, they will not be uniformly distributed, and so our approximation will be poor.

Second, there should be a large number of inputs. The approximation will generally be poor if only a few grains are randomly dropped into the whole square. On average, the approximation improves as more grains are dropped.
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More from Wiki:

Monte Carlo methods vary, but tend to follow a particular pattern:1) Define a domain of possible inputs.2) Generate inputs randomly from a probability distribution over the domain.3) Perform a deterministic computation on the inputs.4) Aggregate the results.

The correct method involves uniformly scattering objects over a square inscribed within a circle, counting objects inside the circle, and then multiplying the ratio by 4 to estimate the value of PI.

Explanation

The correct method involves uniformly scattering objects over a square inscribed within a circle, counting objects inside the circle, and then multiplying the ratio by 4 to estimate the value of PI.

2. How to do numerical integration (know the formula and be able to describe)?

3. One common method for numerical integration is to use the trapezoidal rule to estimate the integral.

2. The formula for numerical integration involves taking the derivative of the function being integrated.

Wiki Source:

In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals. Numerical integration over more than one dimension is sometimes described as cubature,[1] although the meaning of quadrature is understood for higher dimensional integration as well.The basic problem considered by numerical integration is to compute an approximate solution to a definite integral: If f(x) is a smooth well-behaved function, integrated over a small number of dimensions and the limits of integration are bounded, there are many methods of approximating the integral with arbitrary precision.
Reasons for numerical integrationThere are several reasons for carrying out numerical integration. The integrand f(x) may be known only at certain points, such as obtained by sampling. Some embedded systems and other computer applications may need numerical integration for this reason.A formula for the integrand may be known, but it may be difficult or impossible to find an antiderivative which is an elementary function. An example of such an integrand is f(x) = exp(?x2), the antiderivative of which (the error function, times a constant) cannot be written in elementary form.It may be possible to find an antiderivative symbolically, but it may be easier to compute a numerical approximation than to compute the antiderivative. That may be the case if the antiderivative is given as an infinite series or product, or if its evaluation requires a special function which is not available.

1. Numerical integration is used to calculate the area under a curve only when the function is continuous.

The correct answer provides a detailed explanation of numerical integration, its applications, and reasons for use. The incorrect answers are misleading as they do not accurately describe the process of numerical integration or the methods involved.

Explanation

The correct answer provides a detailed explanation of numerical integration, its applications, and reasons for use. The incorrect answers are misleading as they do not accurately describe the process of numerical integration or the methods involved.

3. What is a time series?

A pattern of data points with no correlation to time intervals.

A sequence of random numbers collected over a period of time.

A set of non-numerical data points measured at irregular time intervals.

FINAL ANSWER (GO WITH THIS)!!!!!!!!

A time series is point data at time intervals.

(answer came from June 7th Lecture Notes)

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http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm

Time series analysis accounts for the fact that data points takenover time may have an internal structure (such as autocorrelation, trendor seasonal variation) that should be accounted for.

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http://www.investopedia.com/terms/t/timeseries.asp#axzz1PsyEKLGj

What Does Time Series Mean?
A sequence of numerical data points in successive order, usually occurring in uniform intervals. In plain English, a time series is simply a sequence of numbers collected at regular intervals over a period of time.

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Wiki Source: (http://en.wikipedia.org/wiki/Time_series)

A time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the Nile River at Aswan.

A time series is a sequence of numerical data points in successive order, usually occurring in uniform intervals. It is not random numbers or non-numerical data, and it has a correlation to time intervals.

Explanation

A time series is a sequence of numerical data points in successive order, usually occurring in uniform intervals. It is not random numbers or non-numerical data, and it has a correlation to time intervals.

4. Discuss forecasting accuracy?

Forecasting accuracy only involves formal statistical methods and does not consider judgemental methods.

Forecasting accuracy does not take into account risk and uncertainty, as it aims to predict exact future outcomes.

Wiki Source: (before we look at forecasting accuracy ... let's look at what forecasting is first).
Forecasting is the process of making statements about events whose actual outcomes (typically) have not yet been observed. A commonplace example might be estimation for some variable of interest at some specified future date. Prediction is a similar, but more general term. Both might refer to formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgemental methods. Usage can differ between areas of application: for example in hydrology, the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting and prediction; it is generally considered good practice to indicate the degree of uncertainty attaching to forecasts.

The process of climate change and increasing energy prices has led to the usage of Egain Forecasting of buildings. The method uses Forecasting to reduce the energy needed to heat the building, thus reducing the emission of greenhouse gases. Forecasting is used in the practice of Customer Demand Planning in every day business forecasting for manufacturing companies. The discipline of demand planning, also sometimes referred to as supply chain forecasting, embraces both statistical forecasting and a consensus process. An important, albeit often ignored aspect of forecasting, is the relationship it holds with planning. Forecasting can be described as predicting what the future will look like, whereas planning predicts what the future should look like. There is no single right forecasting method to use. Selection of a method should be based on your objectives and your conditions (data etc.). A good place to find a method, is by visiting a selection tree. An example of a selection tree can be found here.
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Note: (the 4 aspects of this that we need to know are listed below; ex: MAE, MAPE, PMAD, MSE, and RMSE - pick 4 out of the 6 possible aspects/options)

Forecasting accuracyThe forecast error is the difference between the actual value and the forecast value for the corresponding period. where E is the forecast error at period t, Y is the actual value at period t, and F is the forecast for period t.Measures of aggregate error:Mean Absolute Error (MAE) Mean Absolute Percentage Error (MAPE) Percent Mean Absolute Deviation (PMAD) Mean squared error (MSE) Root Mean squared error (RMSE) Forecast skill (SS) Please note that business forecasters and practitioners sometimes use different terminology in the industry. They refer to the PMAD as the MAPE, although they compute this volume weighted MAPE. For more information see Calculating Demand Forecast AccuracyReference class forecasting was developed to increase forecasting accuracy.
Applications of forecastingForecasting has application in many situations:Supply chain management - Forecasting can be used in Supply Chain Management to make sure that the right product is at the right place at the right time. Accurate forecasting will help retailers reduce excess inventory and therefore increase profit margin. Accurate forecasting will also help them meet consumer demand.Weather forecasting, Flood forecasting and MeteorologyTransport planning and Transportation forecastingEconomic forecastingEgain ForecastingTechnology forecastingEarthquake predictionLand use forecastingProduct forecastingPlayer and team performance in sportsTelecommunications forecastingPolitical ForecastingSales Forecasting

Forecasting accuracy refers to the ability to predict the past accurately.

5. What are the key components in C++/Object-Oriented Programming?

(Write the definitionWrite an exampleBe able to identify each of the 5 terms)

Variables, Pointers, Loops, Conditionals

Data types, Functions, Algorithms, Debugging

File handling, Memory management, Exception handling, Templates

C++ and Object-Oriented Programming involve the concepts of classes, inheritance, composition, polymorphism, abstract classes, and interfaces, which are essential for organizing and structuring code in a modular and reusable way.

Explanation

C++ and Object-Oriented Programming involve the concepts of classes, inheritance, composition, polymorphism, abstract classes, and interfaces, which are essential for organizing and structuring code in a modular and reusable way.

6. What is a class in C++?

A class is an expanded concept of a data structure: instead of holding only data, it can hold both data and functions.

An object is an instantiation of a class. In terms of variables, a class would be the type, and an object would be the variable.

Classes are generally declared using the keyword class, with the following format:

class class_name { access_specifier_1: member1; access_specifier_2: member2; ... } object_names;

A class is a data type used to store single values in C++.

A class is a keyword used to define variables in C++.

A class is a function in C++ with specific properties.

In C++, a class is a user-defined data type that holds both data and functions. It serves as a blueprint for creating objects, which are instances of the class.

Explanation

In C++, a class is a user-defined data type that holds both data and functions. It serves as a blueprint for creating objects, which are instances of the class.

7. What is Composition in C++?

Composition is a relationship between two classes that is based on the aggregation relationship. Composition takes the relationship one step further by ensuring that the containing object is responsible for the lifetime of the object it holds. If Object B is contained within Object A, then Object A is responsible for the creation and destruction of Object B. Unlike aggregation, Object B cannot exist without Object A.

Example of Composition (from class):
*add 'Composition' to Shape class
class geoCenter {
private: float x, y;
public:
geoCenter (float x, float y) {
this -> x=x'
this -> y=y;

void setCenter ( );

float getX {return x;}
float getY {return y;}
}

Add to Shape class to make composition (below):

protected:
int givenSize;
geoCenter * origin; //this is a pointer to array

constructor:
Shape{
origin new GeoCenter (0, 0);
}

To Use It:
1) Set center (i, 2i) -- after you instantiate square or cirlce.
2) In 3rd loop, also print center coordinates.

Composition is a type of inheritance in C++.

Composition is a relationship between variables within the same class.

Composition allows an object to exist independently without the containing object.

Composition in C++ is a specific form of object composition which describes a 'has-a' relationship between objects. It differs from inheritance by focusing on the relationship between objects rather than classes.

Explanation

Composition in C++ is a specific form of object composition which describes a 'has-a' relationship between objects. It differs from inheritance by focusing on the relationship between objects rather than classes.

8. What is an Abstract Class in C++?

Define:
Abstract Class - Has virtual methods you implement in a derived class.

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more on abstract classes ...
An abstract class is a class thatis designed to be specifically used as a base class. An abstract class containsat least one pure virtual function. You declare a pure virtual function by using a pure specifier (= 0) in the declaration of a virtual member function in the class declaration.
The following is an example of an abstract class:
class AB {public: virtual void f() = 0;};Function AB::f is a pure virtual function. A function declarationcannot have both a pure specifier and a definition. For example, the compilerwill not allow the following:struct A { virtual void g() { } = 0;};

An abstract class is a class that can only contain private members.

An abstract class is a class that cannot be instantiated.

An abstract class is a class that does not allow inheritance.

An abstract class in C++ is designed to be used as a base class and contains at least one pure virtual function. It cannot be instantiated on its own, and it requires derived classes to implement its virtual methods.

Explanation

An abstract class in C++ is designed to be used as a base class and contains at least one pure virtual function. It cannot be instantiated on its own, and it requires derived classes to implement its virtual methods.

9. Define: Interface in C++

Define:
Interface - A list of methods you implement.

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more on interface ...
A boundary across which two independent systems meet and act on or communicate with each other. In computer technology, there are several types of interfaces. user interface - the keyboard, mouse, menus of a computer system. The user interface allows the user to communicate with the operating system. Also see GUI. software interface - the languages and codes that the applications use to communicate with each other and with the hardware. hardware interface - the wires, plugs and sockets that hardware devices use to communicate with each other. (v.) To connect with or interact with by means of an interface.

A type of computer virus.

The programming language used to write code.

A way to connect hardware devices together.

In C++, an interface refers to a list of methods that a class must implement.

Explanation

In C++, an interface refers to a list of methods that a class must implement.

10. How to read a sequential file (what do we INCLUDE?)

Binary Files

Sequential FilesSequential file techniques provide a straightforward way to read and write files. PowerBASIC's sequential file commands manipulate text files: files of ANSI or WIDE characters with carriage-return/linefeed pairs separating records.
Quite possibly, the best reason for using sequential files is their degree of portability to other programs, programming languages, and computers. Because of this, you can often look at sequential files as the common denominator of data processing, since they can be read by word-processing programs and editors (such as PowerBASIC's), absorbed by other applications (such as database managers), and sent over the Internet to other computers.
The idea behind sequential files is simplicity itself: write to them as though they were the screen and read from them as though they were the keyboard.

Create a sequential file using the following steps:
Open the file in sequential output mode. To create a file in

PowerBASIC, you must use the OPEN statement. Sequential files have two options to prepare a file for output: OUTPUT: If a file does not exist, a new file is created. If a file already exists, its contents are erased, and the file is then treated as a new file.APPEND: If a file does not exist, a new file is created. If a file already exists, PowerBASIC appends (adds) data at the end of that file.
Output data to a file. Use WRITE# or PRINT# to write data to a sequential file.
Close the file. The CLOSE statement closes a file after the program has completed all I/O operations. ======================
To read a sequential file:First, OPEN the file in sequential INPUT mode. This prepares the file for reading.
Read data in from the file. Use PowerBASIC's INPUT# or LINE INPUT# statements.
Close the file. The CLOSE statement closes a file after the program has completed all I/O operations.
The drawback to sequential files is, not surprisingly, that you only have sequential access to your data. You access one line at a time, starting with the first line. This means if you want to get to the last line in a sequential file of 23,000 lines, you will have to read the preceding 22,999 lines.Sequential files, therefore, are best suited to applications that perform sequential processing (for example, counting words, checking spelling, printing mailing labels in file order) or in which all the data can be held in memory simultaneously. This allows you to read the entire file in one fell swoop at the start of a program and to write it all back at the end. In between, the information can be stored in an array (in memory) which can be accessed randomly.Although the SEEK statement can be used to change the point in the file where the next read or write will occur, the calculations required to determine the position of the start of each record in a sequential file would add considerable overhead. Sequential files typically consist of records of varying sizes. Either you would have to maintain a separate index file indicating the starting byte position of each record, or you would have to seek randomly until you found the correct position. However, SEEK does have its uses with sequential files. For instance, after reading an entire file, you could use SEEK to reposition the file pointer to the start of the file, in order to process the data a second time. This is certainly quicker than closing and re-opening the file.Sequential files lend themselves to database situations in which the length of individual records is variable. For example, suppose an alumni list had a comments field. Some people may have 100 bytes or more of comments. Others, perhaps most, will have none. Sequential files handle this problem without wasting disk space.
The OPEN statement provides an optional LEN parameter for use with sequential files. This instructs PowerBASIC to use internal buffering to speed up reading of sequential files, using a buffer of the size specified by the LEN parameter. A buffer of 8192 bytes is suggested for best general performance, especially when networks are involved. However, this value can be increased in size to gain additional performance - the best value will always be specific to a particular combination of hardware and software, and may vary considerably from PC to PC, network to network, etc.
The OPEN statement also provides an optional character mode parameter. This specifies the character mode for this file: ANSI or WIDE (Unicode). Since sequential files consist of text alone, the selected mode is enforced by PowerBASIC. All data read or written to the file is automatically forced to the selected mode, regardless of the type of variables or expressions used. With binary or random files, this specification has no effect, but it may be included in your code for self-documentation purposes.ANSI characters in the U.S. range of CHR$(0) to CHR$(127) are known as ASCII, and are always represented by a single byte. International ANSI characters in the range of CHR$(128) to CHR$(255) may be followed by one or more additional bytes in order to accurately represent non-U.S. characters. The exact definition of these characters depends upon the character set in use. WIDE characters are always represented by two bytes per character. If the Chr option is not specified, the default mode is ANSI.

Indexed Files

Random Files

11. How to read a sequential file (What statements are necessary?)

(SAME AS ABOVE)

Sequential FilesSequential file techniques provide a straightforward way to read and write files. PowerBASIC's sequential file commands manipulate text files: files of ANSI or WIDE characters with carriage-return/linefeed pairs separating records.
Quite possibly, the best reason for using sequential files is their degree of portability to other programs, programming languages, and computers. Because of this, you can often look at sequential files as the common denominator of data processing, since they can be read by word-processing programs and editors (such as PowerBASIC's), absorbed by other applications (such as database managers), and sent over the Internet to other computers.
The idea behind sequential files is simplicity itself: write to them as though they were the screen and read from them as though they were the keyboard.

Create a sequential file using the following steps:
Open the file in sequential output mode. To create a file in

PowerBASIC, you must use the OPEN statement. Sequential files have two options to prepare a file for output:OUTPUT: If a file does not exist, a new file is created. If a file already exists, its contents are erased, and the file is then treated as a new file.APPEND: If a file does not exist, a new file is created. If a file already exists, PowerBASIC appends (adds) data at the end of that file.
Output data to a file. Use WRITE# or PRINT# to write data to a sequential file.
Close the file. The CLOSE statement closes a file after the program has completed all I/O operations.======================
To read a sequential file:First, OPEN the file in sequential INPUT mode. This prepares the file for reading.
Read data in from the file. Use PowerBASIC's INPUT# or LINE INPUT# statements.
Close the file. The CLOSE statement closes a file after the program has completed all I/O operations.
The drawback to sequential files is, not surprisingly, that you only have sequential access to your data. You access one line at a time, starting with the first line. This means if you want to get to the last line in a sequential file of 23,000 lines, you will have to read the preceding 22,999 lines.Sequential files, therefore, are best suited to applications that perform sequential processing (for example, counting words, checking spelling, printing mailing labels in file order) or in which all the data can be held in memory simultaneously. This allows you to read the entire file in one fell swoop at the start of a program and to write it all back at the end. In between, the information can be stored in an array (in memory) which can be accessed randomly.Although the SEEK statement can be used to change the point in the file where the next read or write will occur, the calculations required to determine the position of the start of each record in a sequential file would add considerable overhead. Sequential files typically consist of records of varying sizes. Either you would have to maintain a separate index file indicating the starting byte position of each record, or you would have to seek randomly until you found the correct position. However, SEEK does have its uses with sequential files. For instance, after reading an entire file, you could use SEEK to reposition the file pointer to the start of the file, in order to process the data a second time. This is certainly quicker than closing and re-opening the file.Sequential files lend themselves to database situations in which the length of individual records is variable. For example, suppose an alumni list had a comments field. Some people may have 100 bytes or more of comments. Others, perhaps most, will have none. Sequential files handle this problem without wasting disk space.
The OPEN statement provides an optional LEN parameter for use with sequential files. This instructs PowerBASIC to use internal buffering to speed up reading of sequential files, using a buffer of the size specified by the LEN parameter. A buffer of 8192 bytes is suggested for best general performance, especially when networks are involved. However, this value can be increased in size to gain additional performance - the best value will always be specific to a particular combination of hardware and software, and may vary considerably from PC to PC, network to network, etc.
The OPEN statement also provides an optional character mode parameter. This specifies the character mode for this file: ANSI or WIDE (Unicode). Since sequential files consist of text alone, the selected mode is enforced by PowerBASIC. All data read or written to the file is automatically forced to the selected mode, regardless of the type of variables or expressions used. With binary or random files, this specification has no effect, but it may be included in your code for self-documentation purposes.ANSI characters in the U.S. range of CHR$(0) to CHR$(127) are known as ASCII, and are always represented by a single byte. International ANSI characters in the range of CHR$(128) to CHR$(255) may be followed by one or more additional bytes in order to accurately represent non-U.S. characters. The exact definition of these characters depends upon the character set in use. WIDE characters are always represented by two bytes per character. If the Chr option is not specified, the default mode is ANSI.

Text Files

Binary Files

Random Access Files

The correct answer is 'Sequential Files' because sequential file techniques involve reading and writing files in a sequential manner using specific commands. Random Access Files and Binary Files involve different methods of file manipulation, while Text Files can be used for storing data but do not specifically refer to the process of reading a sequential file.

Explanation

The correct answer is 'Sequential Files' because sequential file techniques involve reading and writing files in a sequential manner using specific commands. Random Access Files and Binary Files involve different methods of file manipulation, while Text Files can be used for storing data but do not specifically refer to the process of reading a sequential file.