Mean lifetime

[roshan2004]

How can we prove that the mean life time of a radioactive decay is reciprocal to the decay constant?

[Astronuc]

How can we prove that the mean life time of a radioactive decay is reciprocal to the decay constant? What is the definition of 'mean lifetime' and how would one describe it mathematically?

Think about the survival time for a population of particles that decay, and how N(t) relates to A(t), where A(t) = dN(t)/dt.