Statistics and Probability

1. Overview

Statistics focuses predominantly on samples and incomplete data. Doing so brings some uncertainty to any of the results we reach. This uncertainty is what leads us to rely on some of the most important concepts of probability like expected values or prediction intervals.

2. Description

2.1 Relation Between Statistics and Probability

In a way, probability lays the groundwork for statistics because it defines terms like mean, variance, or expected value. Statistics tries to analyze numeric and categorical data and see how well it resembles any of the probability.

2.2 Confidence Interval

Many useful concepts based on probability theory. For instance, Confidence interval. CI uses sample data to define a range with an associated degree of certainty. Express the likelihood of the population mean is within that interval. We must know what mean, variance, and standard deviation are thus having a good understanding of probability is crucial.

2.3 Hypothesis Testing

A hypothesis is an idea that can be tested.

The three crucial requirements for conducting successful hypothesis testing are knowing the mean, variance, and type of distribution with the help of these three and some formulas. We can validate similar statements again to a specific degree of certainty all right in the field of statistics.

2.3.1 Choosing a Distribution

We are often provided sample data without knowing the type

• The same logic is often applied in statistics
• any distribution we try on predicts a value for all points within our dataset.
• This is what the distribution anticipates the actual data point to be.
  • So it is essentially a type of anticipated average value.

So the more distributions you know the easier it will be for you to determine which one you're dealing with for a certain problem. After finding the distribution we are dealing with. We like to create different models such as regressions since the mathematics behind regressions is complex and computationally expensive. We use computer software to find the appropriate values. We call this entire process of mathematical modeling.

3. Reference

https://365datascience.com/