# Sum of Discrete Random Variables [duplicate]

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?

• 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 $Z$ Feb 17, 2019 at 13:49
• Assuming independent and not equally likely what will be the answer? Feb 17, 2019 at 13:57
• Much the same, except now the dice are biased towards particular values Feb 17, 2019 at 14:00