Mathematics Asked by dabdya on December 3, 2020
What is the distribution of a random variable $xi$ given on the set of all natural numbers, if $$mathbb P(xi > a + b mid xi > a) = mathbb P(xi > b)$$ $$forall a,b in mathbb N$$
Simplifying the equality, I got $$mathbb P(xi > a + b) = mathbb P(xi > a) mathbb P(xi > b)$$ because $$mathbb P(xi > a + b mid xi > a) = frac{mathbb P(xi > a + b cap xi > a)}{mathbb P(xi > a)} = frac{mathbb P(xi > amid xi > a + b)mathbb P(xi > a + b)}{mathbb P(xi > a)} = frac{mathbb P(xi > a + b)}{mathbb P(xi > a)}$$
After a little thought, I realized that the distribution can be $$S = sum_{i=1}^n frac{1}{2^n}$$ $$lim_{nto infty}S = 1 = p_1 + p_2 + ldots + p_n + ldots$$
But I want to know if it is possible to generalize somehow and find all such distributions and show that there are no others. Thanks.
Get help from others!
Recent Questions
Recent Answers
© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP