A Selection of Problems from A.A. Markov’s Calculus of Probabilities: Problem 8 – Sums of Independent Random Variables

Author(s):

Alan Levine (Franklin and Marshall College)

This problem is very different from the others in this chapter. It is a variation of the material covered in Chapter III, where Markov was concerned with theorems about limiting probabilities, such as the Central Limit Theorem. As with the previous problems, there is ample room for the reader to fill in mathematical details.

Задача 8^ая. Пусть \(X_1, X_2,\dots, X_n\) будуть \(n\) независимых величин и пусть совокупность чисел \(1, 2, 3,\dots, m\) представляет все возможные, и при том равновозможные значения каждой из них.

Требуется найти вероятность, что сумма \(X_1, X_2,\dots, X_n\) будеть равна данному числу.

8^th Problem. Let \(X_1, X_2, \dots, X_n\) be \(n\) independent variables and let the set of numbers \(1,2,3,\dots,m\) represent all possible, equally likely values of each of them.

It is required to find the probability that the sum \(X_1 + X_2 + \cdots + X_n\) will be equal to some given number.

Continue to beginning of Markov's solution of Problem 8.

Skip to Markov's analysis of the binomial distribution.

Alan Levine (Franklin and Marshall College), "A Selection of Problems from A.A. Markov’s Calculus of Probabilities: Problem 8 – Sums of Independent Random Variables," Convergence (November 2023)

Convergence

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History of Mathematics