The sum of two dice

Topic: Random variables and distributions · more questions on this topic
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Two fair dice are thrown in order, and Z is their sum.

1. Write Z as a function on the sample space.

2. Give the probability mass function of Z.

Worked answer (click to show)

1. On the sample space \{1,\ldots,6\}^2, Z(x,y)=x+y.

2. The value z\in\{2,\ldots,12\} occurs in 6-|z-7| of the 36 pairs, so \mathbb{P}(Z=z)=(6-|z-7|)/36.