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If I have two independent discrete random variables, say, $$ X \in \{1,3,10,20\} $$ and $$ Y \in \{2,3,5,9,11,15\} $$ and let $$Z = X + Y $$ be the sum of two variables. Also, each value taken by either random variable is not equally likely. How do I calculate the distribution of $Z$? More importantly, what does it mean to sum two random variables?

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    $\begingroup$ It rather depends on whether $X$ and $Y$ are independent and whether the values are equally likely. If so, you could imagine having two fair dice, one with four sides and the $X$ values and the other with six sides and the $Y$ values; throw the dice and add the two values together to get the sum $Z$ $\endgroup$ – Henry Feb 17 '19 at 13:49
  • $\begingroup$ Assuming independent and not equally likely what will be the answer? $\endgroup$ – KAY_YAK Feb 17 '19 at 13:57
  • $\begingroup$ Much the same, except now the dice are biased towards particular values $\endgroup$ – Henry Feb 17 '19 at 14:00

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