A store opens at 8 A.M. From 8 until 10 customers arrive at a Poisson rate of four an hour. Between 10 and 12 they arrive at a Poisson rate of eight an hour. From 12 to 2 the arrival rate increases steadily from eight per hour at 12 to ten per hour at 2; and from 2 to 5 the arrival rate drops steadily from ten per hour at 2 to four per hour at 5. Determine the probability distribution of the number of customers that enter the store on a given day.
First, i have to find $\lambda (t)$. This is what i did:
For a day, the arrival rate can be written $\lambda (t) = \left\{ \begin{gathered} 0{\text{ if }}0 \leqslant t < 8 \hfill \\ 4{\text{ if 8}} \leqslant t < 10 \hfill \\ 8{\text{ if }}10 \leqslant t < 12 \hfill \\ 0{\text{ if }}17 \leqslant t < 24 \hfill \\ \end{gathered} \right.$
how can i find $\lambda (t)$ for $12 \leqslant t < 14$ and $\lambda (t)$ for $14 \leqslant t < 17$ ? I'am stuck here.