Solved Problems in Probability Theory

In this book titled "Solution Problems in Probability Theory", we have included the original problems we have created as well as the problems in Turkish, Azerbaijani, English and mostly Russian sources. Our main aim in this study is to enrich students' mathematical thinking structures by enabling them to see as many problems as possible. We believe that this problem and exercise book, the first edition of which has been published, will be useful to all students taking probability courses.
In the first part of the book, after giving examples on “Basic Concepts of Probability Theory”, briefly permutation and combination, there are many examples suitable for n >2 dice rolls, especially among the examples suitable for the classical probability definition. In addition, examples that use probability rules related to the combination of at least two events are given weight. The probabilities of independent events, fully independent events and conditional probability, Bayes' theorem and problems complying with the total probability formulas are prepared. Finally, in the first chapter, very comprehensive geometric probability questions are solved.
The second part is devoted to discrete and continuous probability distributions. Bernoulli, binomial, discrete regular, geometric, negative binomial, hyper geometric, Poisson distributions from discrete distributions, regular, exponential, normal, Gamma, Weibull, Beta, Cauchy distributions from continuous distributions are discussed.
In the third chapter, problems on "Numerical and Functional Characteristics of Random Variables" are expressed and their solutions are presented to the reader in the form of exercises. In this section, the expected value, variance, higher order moments, moment generating and characteristic functions of random variables are examined.
We believe that it will be very useful to the faculty members who recommend this book as a supplementary book in our universities and to the students who apply to benefit from it.