So the problem says "Let $X$ be the sum of outcomes of rolling $2$ dice, where the outcome for each dice appears with equal probability. What is the pmf of $X$?"

I got: $X$ could take on any value in the set $\{2,3,4,5,6,7,8,9,10,11,12\}$ The probability mass function is $$f(x) = \begin{cases}\frac1 {36} & \text{ if } x∈{2,12}\\\frac1 {18} & \text{ if } x∈{3,11}\\ \frac1 {12} & \text{ if } x∈{4,10}\\ \frac1 {9} & \text{ if } x∈{5,9}\\\frac5 {36} & \text{ if } x∈{6,8}\\\frac1 {6} & \text{ if } x∈{7}\\ \ 0 & \text{ if } other\end{cases}$$

Is the answer correct? If so, is there any way I can write the answer in a more precise way instead of listing all the values of $x$?

  • $\begingroup$ does the pmf sum to 1? that's typically a good thing to check. $\endgroup$ Jan 14, 2017 at 3:08
  • $\begingroup$ @DanielXiang Yes 1/36*2+2/36*2+3/36*2+4/36*2+5/38*2+6/36=1 $\endgroup$
    – Betty
    Jan 14, 2017 at 3:19

1 Answer 1


Your answer is correct and precise; it may not be concise.

For a more concise answer (which is not always possible, but is possible in this case) try to rewrite each fraction so it has the same denominator $36$, and try to see if there's a formula tying the numerator to the result(s) with that probability!


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