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statistics student t test

The beta distribution represents continuous probability distribution parametrized by two positive shape parameters, $ \alpha $ and $ \beta $, which appear as exponents of the random variable x and control the shape of the distribution. Probability density function Probability density function of Beta distribution is given as: Formula ${ f(x) = \frac{(x-a)^{\alpha-1}(b-x)^{\beta-1}}{B(\alpha,\beta) (b-a)^{\alpha+\beta-1}} \hspace{.3in} …

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statistics stratified sampling

A measure of the accuracy of a test or measuring instrument obtained by measuring the same individuals twice and computing the correlation of the two sets of measures. Reliability Coefficient is defined and given by the following function: Formula ${Reliability\ Coefficient,\ RC = (\frac{N}{(N-1)}) \times (\frac{(Total\ Variance\ – Sum\ of\ Variance)}{Total Variance})}$ Where − ${N}$ …

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statistics notations

Regression Intercept Confidence Interval, is a way to determine closeness of two factors and is used to check the reliability of estimation. Formula ${R = \beta_0 \pm t(1 – \frac{\alpha}{2}, n-k-1) \times SE_{\beta_0} }$ Where − ${\beta_0}$ = Regression intercept. ${k}$ = Number of Predictors. ${n}$ = sample size. ${SE_{\beta_0}}$ = Standard Error. ${\alpha}$ = …

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statistics stem and leaf plot

In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. Relative Standard Deviation, RSD is defined and given by the following probability function: Formula ${100 \times \frac{s}{\bar x}}$ Where − ${s}$ = the sample standard …

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statistics formulas

The Rayleigh distribution is a distribution of continuous probability density function. It is named after the English Lord Rayleigh. This distribution is widely used for the following: Communications – to model multiple paths of densely scattered signals while reaching a receiver. Physical Sciences – to model wind speed, wave heights, sound or light radiation. Engineering …

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statistics skewness

Process sigma can be defined using following four steps: Measure opportunities, Measure defects, Calculate yield, Look-up process sigma. Formulae Used ${DPMO = \frac{Total\ defect}{Total\ Opportunities} \times 1000000}$ ${Defect (\%) = \frac{Total\ defect}{Total\ Opportunities} \times 100}$ ${Yield (\%) = 100 – Defect (\%) }$ ${Process Sigma = 0.8406+\sqrt{29.37}-2.221 \times (log (DPMO)) }$ Where − ${Opportunities}$ = …

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