Question

Briefly describe the following concepts/principles/items, use appropriate diagrams/equations/formulas/examples if needed:

                i.          Gaussian curve

               ii.          Coefficient of variation

              iii.          Confident interval

             iv. Q test

               v.          Dialysis

Answer 1

Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value μ = b and variance σ² = c². In this case, the Gaussian is of the form

The Gaussian curve is the curve of the density function of the normal distribution.

For , we get the Gaussian curve said to be "standard".

Cartesian Equation:

giving the number of individuals of height between x and x + dx in a "normal" population of N people, with mean height m and a standard deviation s.

For example, the number of subsets with k elements of a set with n elements can be approximated for large values of n by f(k) with

The area between the curve and the asymptote is equal to N; the area of the portion between m - s et m + s is approximately equal to 2/3 of N; between m - 2s and m + 2s it is approximately 96% of N.

Cartesian equation: ; coordinates of the flex points : .
The area between the curve and the asymptote: ; centroid of this domain : .

B) Coefficient of Variation

The coefficient of variation (CV) is a factual proportion of the scattering of information that focuses on an information arrangement around the mean. The coefficient of variety speaks to the proportion of the standard deviation to the mean, and it is a valuable measurement for looking at the level of variety starting with one information arrangement then onto the next, regardless of whether the methods are definitely not the same as each other.

The coefficient of Variation shows the degree of variability of information in an example corresponding to the mean of the populace. In fund, the coefficient of variety permits speculators to decide how much instability, or hazard, is accepted in contrast with the measure of return anticipated from ventures. In a perfect world, the coefficient of variety equation should bring about a lower proportion of the standard deviation to mean return, which means the better hazard return compromise. Note that if the normal return in the denominator is negative or zero, the coefficient of variety could be deceiving.

The coefficient of Variation is useful when utilizing the hazard/reward proportion to choose speculations. For instance, a financial specialist who is chance opposed might need to consider resources with a verifiably low degree of volatility and a serious extent of return, according to the general market or its industry. On the other hand, chance looking for speculators may hope to put resources into resources with a truly serious extent of unpredictability.

While regularly used to break down scattering around the mean, quartile, quintile, or decile CVs can likewise be utilized to comprehend variety around the middle or tenth percentile.

the formula for how to calculate the coefficient of variation:

CV=σ / μ​

where:σ=standard deviation

μ=mean​

C) Confident Interval

A Confidence Interval is a range of values we are genuinely certain our true value lies in.

Confidence interval (CI) is a sort of estimate computed from the insights of the watched information. This proposes a scope of conceivable qualities for an unknown parameter (for a model, the mean). The span has an associated confidence level that the genuine boundary is on the proposed extend. Given observations   and a confidence level , a legitimate certainty stretch has a probability of containing the genuine hidden boundary. The degree of certainty can be picked by the agent. When all is said in done terms, a certainty stretch for an obscure boundary depends on inspecting the distribution of a corresponding estimator.

the certainty level speaks to the frequency (i.e. the extent) of conceivable certainty stretches that contain the genuine estimation of the obscure populace boundary. As it were, if certainty stretches are built utilizing a given certainty level from an unbounded number of autonomous example measurements, the extent of those spans that contain the genuine estimation of the boundary will be equivalent to the certainty level.

The certainty level is assigned before looking at the information. Most ordinarily, a 95% certainty level is used. However, certainty levels of 90% and 99% are likewise frequently utilized in the investigation.

Elements influencing the width of the certainty span incorporate the size of the example, the certainty level, and the inconstancy in the example. A bigger example will in general produce a superior gauge of the populace boundary, when every single other factor are equivalent. A higher certainty level will in general produce a more extensive certainty span.