MathDB

Let

p_0,p_1,\ldots

be a probability distribution on the set of nonnegative integers. Select a number according to this distribution and repeat the selection independently until either a zero or an already selected number is obtained. Write the selected numbers in a row in order of selection without the last one. Below this line, write the numbers again in increasing order. Let

A_i

denote the event that the number

i

has been selected and that it is in the same place in both lines. Prove that the events A_i \;(i\equal{}1,2,\ldots) are mutually independent, and P(A_i)\equal{}p_i. T. F. Mori

Problem Statement