Chapter 15.6, Problem 5P

The probability for a radioactive particle to decay between time $t$ and time $t+dt$ is proportional to $e^{-\lambda t}.$ Find the density function $f(t)$ and the cumulative distribution function $F(t).$ Find the expected lifetime (called the mean life) of the radioactive particle. Compare the mean life and the so-called "half life" which is defined as the value of $t$ when $e^{-\lambda t}=1/2$.