PROBABILITY THEORY ASSIGNMENT HELP

PROBABILITY THEORY ASSIGNMENTS HELP

Axiomatic Approach to Probability Theory:

Although there is not much objection against the logical content of the frequency approach for defining probability there is some inherent weakness or inelegance in the mathematical formalism. In the definition, we note that the frequency ratio is thoroughly an empirical concept, whereas the limit is postulated in a rigorous analytical sense. This combination of empirical and theoretical concepts is very inelegant and naturally leads to mathematical difficulties. Now this problem is not typical of probability theory only but arises in other branches of mathematics as well. In the theory of probability also, we are ultimately forced to give up the hope of defining probabilities and take resources to an axiomatic theory in which probability is accepted as an undefined new concept, and only the salient rules for the calculation of probabilities are postulated. These rules will, however, be chosen from the previous theories with necessary modification for operational convenience.

Axioms of Probability:

The axiomatic approach to probability was proposed by A.N. Kolmogorov in the year 1933. When this approach is followed, no precise definition of probability is given, rather we give certain axioms or postulates on which probability calculations are based.

Baye’s Theorem:

Baye’s Theorem for evaluating new information and revising our prior estimates of the probability. If correctly used, it makes it unnecessary to gather masses of data over long periods of time in order to make good decisions based on probabilities.

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PROBABILITY ASSIGNMENT HELP

PROBABILITY ASSIGNMENT HELP

Many phenomena of business, economics, and social science possess uncertainly, but the outcomes may not always be the same even under the same set of circumstances. They lack deterministic regularity in their outcomes. In our day to day life, we also use the concept of probability, for example, it might rain today, probably the price of X share will go up, probably ‘X’ team will win the match, there are good chances that our sales will go up by 10 percent next year, our company may cross the target profit this year. All these terms may, probably, likely, convey the same sense, i.e., the events are not certain to occur. It connotes the sense that there is uncertainty about the happening of an event. The probability theory has its origin in the game of chances relating to gambling, such as tossing a coin, throwing dice, drawing a card from a pack of cards, etc. Over the year, different authorities contributed to developing the probability theory, namely Galileo. Probability theory is being applied in decision-making in economics, business, political, social, medicine, insurance, etc. Probability is a language in which we discuss uncertainty before one can communicate with another in this language.

Experiment, Outcomes, Events, and Sample Space:

Probability in common Parlance canoes the chances of occurrence of an event or happening. A process that could lead to two or more two different outcomes and uncertainty as to which outcome will occur is called an experiment. For example:

  • Tossing of a coin
  • Rolling a dice
  • Voters preference for a candidate
  • Launching of a new product in the market
  • Asking worker whether he has joined the trade union.

 

All these processes have three features:

 

  • First, there are two or more two possible outcomes.
  • It is possible to specify all the outcomes in advance.
  • There is uncertainty about the outcomes or happening.

Any process which has all three features is called a random experiment in probability theory terminology. 

Classical Approach:

The classical approach to probability is the oldest and simplest one. It originated from chances like tossing a coin, throwing a dice, pack of cards, etc. It is based on considerations of symmetry and logic. The basic assumption in the classical approach is, the outcomes are ‘equally likely,’ e.g., tossing a coin, there are equal chances of Head and tail.

Subjective Probability Approach

Subjective probabilities are based on the beliefs of the person making probability assessments. Thus it may differ from person to person or from time for the same person. In subjective probability, an assessment individual makes estimates based on experience and education. Sometimes it might be hunches or intuition. For example, management is interested in knowing the probability of a major nuclear accident at this location. In these situations, neither the classical nor relative frequency approach helps in calculating the probabilities.

Probability Rules:

Decision-makers who use probabilities are concerned with two conditions: –

  • The case where one event or another event will occur, i.e., probability of either A or event B.
  • The case where two or more events will occur simultaneously, i.e., probability of occurrence of events A and B

 

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NORMAL DISTRIBUTION ASSIGNMENT HELP

NORMAL DISTRIBUTION ASSIGNMENT HELP

The random variables that can take any value on a continuum. It has a infinite or uncountable infinite number of values on its sample space. Such random variables are continuous distributions. Many types of data are continuous in nature because the observations are obtained by measurements such as time, distance, or temperature, heights, weight etc. In continuous variables, the successive observations may differ by infinitesimal amounts. Any random variable whose values are measured as a continuous variable it is counted. The probabilistic model of a continuous variable involves the selection of a curve usually smooth called the probability distribution or probably density function. The distributions may assume a variety of shapes. It is interesting to note that very large numbers of random of random variables observed in nature possess a curve which is approximately bell shaped and is commonly referred as normal probability distribution. This occupies a central position in statistical inference theory and is widely applied in practical situations.

Significance of Normal Distribution:

 

  • Large Number of phenomenons tends to follow a normal distribution pattern. Numerous variables tend to follow a pattern of variation that is similar to the normal distribution. Natural traits such as heights, weights, I.Q. of children, test scores in an exam, life of electric lamp, breaking strength of a steel rope, errors of measurement, life of an automobile tyre etc. can be approximated through normal distribution.
  • Sampling distribution of many sampling statistics such as mean has an approximately normal distribution. Many distributions in business, economic, sociology and other social sciences do not resemble the normal distribution but the distribution of sample means in each case, usually is normal as long as the sample size is large. This property has a wide application in sampling estimation and testing of hypothesis.
  • Other types of sampling distribution can be approximated by normal function. In the previous chapter, we observed that binomial, and Poisson distribution approach to normal distribution when the value of ‘n’ is very large. It is too laborious to work out the probabilities for a binomial random variable or Poisson variable when ‘n’ is very large. In these conditions, normal distribution can be used as approximation to binomial distribution.

 

Normal Curve:

The shape of the normal curve is bell-shaped. The curve has a single peak thus it is unimodel. The mean of a normally distributed population lies at the center of its curve. Because of the symmetry, the median (Positional average) a mode (concentration of frequency) also lies at the center. Thus in normal distribution mean, median, and mode all coincide. The two tails of the curve extend indefinitely and never touches the X-axis.

Properties of Parameters:

There are only two parameters of normal distribution i.e. mean (μ) and variance (σ2). The mean determines the location of the curve and variance determines the shape of the curve. Given variance, a change in mean will shift the curve as a whole along the x-axis. The following figure depicts the three normal curves, having the same variance but different means.

Standard Normal Distribution

In this sub-section, we will study how a particular normal distribution is transformed into standard normal distribution. This special distribution has a mean 0 and a standard deviation of 1 and is written as N (0, 1).

  • The standard normal distribution is the distribution of another normal variable called Z-scores, which is defined as,
  • z = (X-μ)/σ

The Z – score is the difference of an observation X from the mean (μ) expressed in term of standard deviation (σ). It is called Z-scores because random variable take on many different units of measures. Since we use only one table which should be standard unit and is represented by 7 this table gives the value or area of probability between variable and mean.

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DATA RESEARCH ASSIGNMENT HELP

DATA RESEARCH ASSIGNMENTS HELP

Research data is information that is collected or created for the purposes of analysis so as to produce results. Several processes can be used in generating research data for different purposes. Research data can be qualitative or quantitative and may be available in print, physical or digital formats. Most researchers create and use data in digital form.

Research can be performed using existing data or through the collection or creation of new data. Among the processes through which data can be generated include experimentation, observation, simulation, compilation or derivation, and referencing. Research data covers a wide range of information types including documents and spreadsheets, database contents, contents of an application, models and algorithms, methodologies and workflow, protocols, and standard operating procedures among others.

Proper management and organization of research data are crucial to ensure accessibility and usability of research, avoid unnecessary duplication and enable validation of the results when necessary. The basic concepts involved are data storage, protection, analysis, sharing, and data reporting

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DESCRIPTIVE STATISTICS ASSIGNMENT HELP

DESCRIPTIVE STATISTICS ASSIGNMENTSS HELP

Descriptive Statistics is the use of statistical techniques to describe data, thereby enabling you to:

  • Distinguish between measures of central tendency, a measure of variability, measures of shape, and measures of association.
  • Understand the meaning of mean, median, mode, quartile, percentile, and range.
  • Compute mean, median, mode, percentile, quartile, range, variance, standard deviation, and mean absolute deviation on ungrouped data.
  • Differentiate between a sample and population variance and standard deviation.
  • Understand the meaning of standard deviation as it is applied by using the empirical rule and Chebyshev’s theorem.
  • Compute the mean, mode, standard deviation, and variance on grouped data.
  • Understand skewness, kurtosis, and box and whisker plots.
  • Compute a coefficient of correlation and interpret it.

 

The measure of Central Tendency:

 

  • Ungrouped Data: One type of measure that is used to describe a set of data is the measure of central tendency.
  • Mode: The mode is the most frequently occurring value in a set of data.
  • Median: The median is the middle value in an ordered array of numbers.
  • Mean: The arithmetic mean is the average of a group of numbers and is computed by summing all numbers and dividing by the number of numbers.
  • Percentiles: Percentiles are measures of central tendency that divide a group of data into 100 parts.
  • Quartiles: Quartiles are measures of central tendency that divide a group of data into four subgroups of parts.

 

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DATA ANALYSIS ASSIGNMENT HELP

DATA ANALYSIS ASSIGNMENTS HELP

Data analysis is the process of examining information in order to identify relationships or patterns among variables and predict outcomes.

There are two types of data analysis; Qualitative and quantitative analysis. The qualitative analysis aims to give an in-depth understanding of underlying factors while quantitative analysis involves quantification of data so as to generalize and infer results.

The choice of data analysis tool depends on the scale of measurement of the data; whether nominal, ordinal interval or ratio. A nominal scale is used for labeling variables without any quantitative value. An ordinal scale places significance on the order of the values but not the difference between each one. An interval scale is where both the order and the exact difference between values are known. Finally, the ratio scale gives information on the order and exact differences between values and it also allows for a wide range of both descriptive and inferential statistics to be applied.

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DATA MINING ASSIGNMENT HELP

DATA MINING ASSIGNMENTS HELP

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Data Mining is a field of intersection between statistics and computer science. For obvious reasons studying this subject carries extreme importance for students pursuing their academic career in statistics. Besides the raw analysis step, the subject syllabus includes different types of database and data management aspects, different levels of data preprocessing, interestingness metrics, model and inference contemplations, difficulty considerations, post-processing of open structures, visualization, as well as varied types of online updating.

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Business Analytics Assignment Help

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Business Analytics

Business Analytics

Business analytics (BA) is a process applied by organizations to manage large sets of data so as to produce useful information for problem-solving, and decision making to enhance the performance of the business. Business intelligence, data mining, and analytic applications are well integrated within transactional systems to facilitate analytics.

The process of analytics involves three major component sequential steps. The first step is a descriptive-analytic analysis where data is sorted into groups to improve manageability. Predictive analysis uses historical data to determine whether observed trends can be used to predict the future. The final step; prescriptive analysis helps users to come up with different possible outcomes to guide towards solutions and optimal utilization of resources based on the predicted future trends.

Many organizations take up BA as a routine so as to address specific issues, while other firms use it as a guide to planning through exploration and discovery of new knowledge. BA is applied in several aspects of a firm including sales and marketing, fraud detection, and supply chain optimization.

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BUSINESS INTELLIGENCE ASSIGNMENT HELP

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Business intelligence (BI) is a process for data analysis and presentation purpose to assist business executives and managers in decision making. BI uses a number of important tools, applications, and methods that make it possible for an organization to collect data, develop queries and run them against the data, report generation, data visualization and this helps in making the data information available to the corporate members when making informed decisions.

Business intelligence is important in corporate organizations as they help in accelerating and improving decision-making processes, optimize efficiency, increase potential revenues as well a higher competitive advantage in the industry. Business Intelligence has also been used by companies to do market research and identify the potential market segments as well as analyze the trends, this helps in improving on their weak points.

Business intelligence can include a range of data analysis tools among them enterprise reporting, online analytical processing, and ad hoc analysis. It also incorporates data visualization software for the purpose of developing charts and other infographics as needed.

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