EX 3.4 batteries again

• Consider an experiment in which 9-volt batteries are tested until one with an acceptable voltage ($S$) is obtained.
• The sample space is $\mathcal{S}=\{S,FS,FFS,\dots \}$.
• Define a random variable (rv) $X$ as follows:
  • $X=$ the number of batteries tested before the experiment terminates.
• Observed values of $X$ based on outcomes:
  • $X(S)=1$
  • $X(FS)=2$
  • $X(FFS)=3$
  • …
  • $X(FFFFFFS)=7$
• Any positive integer is a possible value of $X$.
  • Therefore, the set of possible values is infinite.