Question: Assuming that the durations of the two phases are independent of one another, use the convolution formula to show that the total duration T of such a call has probability density function

fT ( t ) =(e^(-t\β 2) -e^(-t\β 1))\β 2-β 1 (0 < t < ∞ ), provided β 1 ≠ β 2, but

fT ( t )=(te^(-t\β))\(β^2) if β 1 = β 2 = β , and prove that both of these functions are legitimate probability density functions.