Let $T_1$ be the waiting time until the first call in a call center and let $T_2$ be the waiting from the first call until the second call.
Assume that both $T_1$ and $T_2$ have an exponential distribution with expectation $0.1$ minutes. Furthermore, $T_1$ and $T2$ are independent.
Derive the probability density function of $Z = T_1 + T_2$.
Since $E[T_1]=E[T_2]=1/10$, $T_1$ and $T_2$ have a $Exp(10)$ distribution, each with a probability density function of $f(x)=10*e^{-10*x}$, then how can I determine the probability density function of the sum?
I tried to add both but it doesn't work, can someone help me please? Thanks in advance!!