Summary
In this chapter, the data scientist approach to probability was shown. Probability concepts was not presented as a mathematical exercise, but some of the most important theorems when working with samples have been shown by simulation: the law of large numbers and the central limit theorem.
The concept of convergence of a mean was shown by tossing a coin. To toss a coin is something very basic in statistics. Think on selecting a person from a sampling frame or not. The Binomial but also the Poisson distribution can be motivated from this. The binomial distribution was shown in this chapter.
Both concepts—the law of large numbers as well as the central limit theorem, lead to confidence intervals, that are—in classical statistics—just a definition. This concept works as soon as the central limit theorem holds.
Also in content of this chapter were the properties of estimators. Bias, unbiasedness, asymptotic unbiasedness, and so on, have been introduced. These wordings will be consequently...
