Given below are two statements:
Statement $I$: The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is directly proportional to the total number of nuclei in the sample.
Statement $II$: The half-life of a radionuclide is the time required for the number of radioactive nuclei to reduce to half of its initial value at time $t = 0$.
In the light of the above statements, choose the most appropriate answer from the options given below:

• A
  Both Statement $I$ and Statement $II$ are correct
• B
  Both Statement $I$ and Statement $II$ are incorrect
• C
  Statement $I$ is correct but Statement $II$ is incorrect
• D
  Statement $I$ is incorrect but Statement $II$ is correct