# An Introduction to Mathematical Statistics

• Yu. A. Rozanov
Part of the Mathematics and Its Applications book series (MAIA, volume 344)

## Abstract

According to a common belief, the birth of a girl or of a boy are equiprobable events. Let us adopt this as the initial hypothesis, and check how it fits some available data. For example, in the period 1871–1900 there were n = 2, 644, 757 babies born in Switzerland including m = 1, 359, 671 boys and nm = 1, 285, 086 girls.* How well does this data agree with our hypothesis that the probability of a boy’s birth is 0.5? By calling the last event a ‘success’, let us discuss the data in the framework of n = 2, 644, 757 Bernoulli trials, with unknown success probability p; the corresponding frequency is
$$\frac{m}{n} = \frac{{1,359,671}}{{2,644,757}} = 0.5141.$$

## Keywords

Decision Rule Mathematical Statistic Independent Random Variable Fisher Information Joint Probability Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Authors and Affiliations

• Yu. A. Rozanov
• 1
1. 1.Steklov Mathematical InstituteMoscowRussia