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Suppose a random variable X can take any value in the interval [−1,2] and a random variable Y can take any value in the interval [−2,3] .

I know that X + Y is [-3, 5] (-1 - 2 = -3; 2+3 = 5) and X - Y is [-4, 4] (-1 - 3 = -4 ; 2 - (-2) = 4) . But where can I find more about the rules of these operations? Like X*Y or X/Y ? And why is this? I thought was something like this:

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João Vitor Gomes
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    Finding the bounds is called "interval analysis" in the numerical computing literature. The duplicate provides a quick introduction and reference. Alternatively, you might be asking about the (usual) [algebra of random variables,](https://en.wikipedia.org/wiki/Algebra_of_random_variables) where [the sum corresponds to convolution,](https://stats.stackexchange.com/questions/331973) etc. and the aim is to compute or analyze the *distributions* of the combined random variables. – whuber Jun 03 '20 at 02:04
  • Thank you again Whuber for the guidance! – João Vitor Gomes Jun 03 '20 at 13:34

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