Probability & Statistics Ch.2 Section 1 Question 4

Solutions for “Probability and Statistics: The Science of Uncertainty” (Second Edition). These are solutions I have come up with; I offer no guarantee of accuracy.

Question

Consider rolling a fair six-sided die, so that $S=\{1,2,3,4,5,6\}$ . Let $X(s)=s$ , and $Y(s)=s^3+2$ . Let $Z=XY$ . Compute $Z(s)$ for all $s\in S$ .

Solution

Z(1)=X(1)\times Y(1) = 1\times (1^3+2) = 1\times 3 = 3

Z(2)=X(2)\times Y(2) = 2\times (2^3+2) = 2\times 10 = 20

Z(3)=X(3)\times Y(3) = 3\times (3^3+2) = 3\times 29 = 87

Z(4)=X(4)\times Y(4) = 4\times (4^3+2) = 4\times 66 = 264

Z(5)=X(5)\times Y(5) = 5\times (5^3+2) = 5\times 127 = 635

Z(6)=X(6)\times Y(6) = 6\times (6^3+2) = 6\times 218 = 1308