I have $(X_i, Y_i)$ as random vectors for $i=1,2,3,\dotsc, 10$. All $X_i$'s and $Y_i$'s are uniformly distributed. My question is about the definition of $R$ which is a random variable such that $R=1(X_i, Y_i)$. $(X_i, Y_i)$ here is a subscript of 1. I just do not know what 1 means. Thanks.

  • $\begingroup$ Yes, I think that makes sense in the context of the problem I am working on. Thank you! $\endgroup$
    – user164144
    Commented Jun 6, 2017 at 3:00

1 Answer 1


I think this is the indicator function. A indicator function equals 1 when the condition is true, zero otherwise.

$$1_A = \begin{cases} 1 & \quad \text{if } A \text{ is true}\\ 0 & \quad \text{otherwise}\\ \end{cases} $$


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