academic tutorials

academic tutorials

statistics standard deviation

Quadratic regression is deployed to figure out an equation of the parabola which can best fit the given set of data. It is of following form: ${ y = ax^2 + bx + c \ where \ a \ne 0}$ Least square method can be used to find out the Quadratic Regression Equation. In this […]

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academic tutorials

statistics signal to noise ratio

Point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a “best guess” or “best estimate” of an unknown (fixed or random) population parameter. More formally, it is the application of a point estimator to the data. Formula ${MLE = \frac{S}{T}}$ ${Laplace = […]

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academic tutorials

statistics simple random sampling

Process Capability Process capability can be defined as a measurable property of a process relative to its specification. It is expressed as a process capability index ${C_p}$. The process capability index is used to check the variability of the output generated by the process and to compare the variablity with the product tolerance. ${C_p}$ is […]

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academic tutorials

statistics shannon wiener diversity index

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value. Probability density function is defined by following formula: ${P(a \le X \le b) = \int_a^b f(x) d_x}$ Where − ${[a,b]}$ = Interval […]

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academic tutorials

statistics sampling methods

For Independent Events The theorem states that the probability of the simultaneous occurrence of two events that are independent is given by the product of their individual probabilities. ${P(A\ and\ B) = P(A) \times P(B) \\[7pt] P (AB) = P(A) \times P(B)}$ The theorem can he extended to three or more independent events also as […]

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academic tutorials

statistics scatterplots

One of the most significant developments in the probability field has been the development of Bayesian decision theory which has proved to be of immense help in making decisions under uncertain conditions. The Bayes Theorem was developed by a British Mathematician Rev. Thomas Bayes. The probability given under Bayes theorem is also known by the […]

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academic tutorials

statistics root mean square

Probability Probability implies ‘likelihood’ or ‘chance’. When an event is certain to happen then the probability of occurrence of that event is 1 and when it is certain that the event cannot happen then the probability of that event is 0. Hence the value of probability ranges from 0 to 1. Probability has been defined […]

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academic tutorials

statistics sample planning

For Mutually Exclusive Events The additive theorem of probability states if A and B are two mutually exclusive events then the probability of either A or B is given by ${P(A\ or\ B) = P(A) + P(B) \\[7pt] P (A \cup B) = P(A) + P(B)}$ The theorem can he extended to three mutually exclusive […]

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academic tutorials

statistics residual sum of squares

Whenever a hypothesis test is conducted, we need to ascertain that test is of high qualitity. One way to check the power or sensitivity of a test is to compute the probability of test that it can reject the null hypothesis correctly when an alternate hypothesis is correct. In other words, power of a test […]

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academic tutorials

statistics required sample size

Poisson conveyance is discrete likelihood dispersion and it is broadly use in measurable work. This conveyance was produced by a French Mathematician Dr. Simon Denis Poisson in 1837 and the dissemination is named after him. The Poisson circulation is utilized as a part of those circumstances where the happening’s likelihood of an occasion is little, […]

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