TITLE: Double dixie cup problem doubt
QUESTION [3 upvotes]: I am reading this article: https://faculty.wharton.upenn.edu/wp-content/uploads/2012/04/Double-dixie-cup-problem.pdf
I have problem with this sentence:
"Let $p_i$ be the probability of failure of obtaining m sets up to and including the purchase of the i_th dixie cup. Then the expected number of dixie cups $E_m(n)= \sum_{i=0}^{\inf}p_i$, by a well-known argument ([1] p. 211)."
The reference is: "W. Feller, Introduction to Probability Theory, vol.I"
But in my version of the book at page 211 contains a different subject.
Can someone help me with this "well-know argument"?

REPLY [2 votes]: If $(X_i)_i$ is a sequence of Bernoulli random variables then the number of successes is $S:=\sum_{i=1}^{\infty}X_i$.
Then by linearity of expectation: $$\mathbb ES=\sum_{i=1}^{\infty}\mathbb EX_i=\sum_{i=1}^{\infty}p_i$$
where $p_i:=P(X_i=1)$.
Does this help (I did not read the article)?
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