EX 3.3 pumps of gas stations again

• EX 2.3 pumps of gas stations describes an experiment to determine the number of pumps in use at two six-pump gas stations.
• Define random variables (rv’s) as follows:
  • $X=$ the total number of pumps in use at the two stations.
  • $Y=$ the difference between the number of pumps in use at station 1 and station 2.
  • $U=$ the maximum number of pumps in use at the two stations.
• If the experiment results in $\omega =(2,3)$:
  • $X\left((2,3)\right)=2+3=5$, so the observed value of $X$ is $x=5$.
  • The observed value of $Y$ is calculated as:
    • $Y=2-3=-1$, so $y=-1$.
  • The observed value of $U$ is:
    • $U=\max (2,3)=3$, so $u=3$.