Briefly explain the meaning of the following terms. Provide at least one relevant example Interval Estimate Point etsimate
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
Briefly explain the
Interval Estimate - Point etsimate
In statistics, estimation refers to the procedure through which inferences are made about a population, based on information obtained from a sample.
Statisticians use sample statistics to estimate the unknown population parameter. For example, sample means are used to estimate population means; sample proportions, to estimate population proportions.
An estimate of a population parameter may be expressed in two ways:
- Point estimate. A point estimate of a population parameter is a single value of a statistic. For example, the sample means is a point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P.
- Interval estimate. An interval estimate is defined by two numbers, between which a population parameter is expected to lie. For example, a < x < b is an interval estimate of the population mean μ. It indicates that the population mean is greater than 'a' but less than 'b'.
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