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### Sum of N random variables from the same distributions [duplicate]

Given $n$ independent random variables from the same distribution, how to obtain the distribution of their sum? For example, the distribution of $n$ normal distribution is $N(n\mu, n\delta^2)$. ...
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 ...