Probability & Statistics Ch.2 Section 1 Question 3

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

Let $S=\{1,2,3,4,5\}$.

a) Define two different (i.e., nonequal) nonconstant random variables X and Y on S.

b) For the random variables X and Y that you have chosen, let $Z=X+Y^2$. Compute $Z(s)$ for all $s\in S$.

Solution

There are infinitely many possible solutions; below is just one I came up with.

(a) Define two different 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 $s\in S$