In the book "Introduction to Probability Models" the author Ross explains the independence on two events, and then extends it to more than two events. I think understand the idea, e.g. all possible combinations of the events must hold the equation below to say they are mutually independent. What I do not understand is the usage of apostrophes. Why is he using apostrophes in the paragraph below?

The definition of independence can be extended to more than two events. The events $E_1, E_2,...,E_n$ are said to be independent if for every subset $E_{1'},E_{2'},E_{3'},...,E_{r'}$, $r\leq n$, of these events


In other words, what is the difference between $E_1$ and $E_{1'}$?

If you can provide a small example it would be very nice.

Thanks a lot.

  • 1
    $\begingroup$ That's a funny notation..but all it means is that $E_{1'}$ is the first element of the subset in question. The subset might be $\{E_3,E_5\}$ say...in which case $E_{1'}=E_3$ and $E_{2'}=E_5$. $\endgroup$
    – lulu
    Commented Feb 20, 2016 at 18:59
  • $\begingroup$ Oh. I see. Thanks a lot. $\endgroup$
    – O. Altun
    Commented Feb 20, 2016 at 19:12

1 Answer 1


Community wiki answer so the question can be marked as answered:

As pointed out in a comment, the notation is unusual. A more usual way to write this would be $E_{k_1},\ldots,E_{k_r}$ (with all $k_i$ different).


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