Chapter 2 Section 1 Question 3
Question
Let $S=\{1,2,3,4,5\}.$
  1. Define two different(i.e., nonequal) nonconstant random variablesm X and Y, on S.
  2. For the random variables X and Y that you have chosen, let $Z=X+Y^2$. Compute Z(s) for all $s\in S$.
Answer
Author: Mohammad-Ali Bandzar| Date:Oct 13 2020
There are infinite many possible solutions below is just one i came up with,
(a) Define two different(i.e., nonequal) nonconstant random variables X and Y, on S.
Let $X(s)=s+1$ and Y(s)=s+2
(b) Let $Z=X+Y^2$. Compute Z(s) for all $s\in S$
$$Z(1)=(s+1)+(s+2)^2$$ $$Z(1)=2+(3)^2$$ $$Z(1)=11$$ $$Z(2)=(s+1)+(s+2)^2$$ $$Z(2)=3+(4)^2$$ $$Z(2)=19$$ $$Z(3)=(s+1)+(s+2)^2$$ $$Z(3)=4+(5)^2$$ $$Z(3)=29$$ $$Z(4)=(s+1)+(s+2)^2$$ $$Z(4)=5+(6)^2$$ $$Z(4)=41$$ $$Z(5)=(s+1)+(s+2)^2$$ $$Z(5)=6+(7)^2$$ $$Z(5)=55$$