probability questions (wait time) Let T be the waiting time in hours when we order a manually scheduled phone call to Timbuktu. The variable T has the probability density (picewise function)
f(t)=k(4-t)   for  0<t<=4;
otherwise f(t)=0
K is a fixed number.
a) Determine the value of the constant k.
b)We booked a conversation with Timbuktu, and we have already had to wait for an hour without the call happened. What is now the conditional probability that the call will happen during the next half hour?
c) on all consecutive days during the same week we will call a specific phone number in timbuktu. What is the expected total wait time for all calls?
I am pretty much cluesless on c, dont really know how to go about a and b.. any tips/solutions? thanks in advance :D

a) We need to have
$$\int_0^4 k(4-t)\,dt=1.$$
Integrate. You should end up concluding that $k=\frac{1}{8}$.
b) Let $A$ be the event that the waiting time is between $1$ and $1.5$, and $B$ the event the waiting time is $\gt 1$. We want $\Pr(A|B)$. By the definition of conditional probability, this is $\frac{\Pr(A\cap B)}{\Pr(B)}$.
For $\Pr(A\cap B)$, we want the probability that $1\le T\lt 1.5$. This is 
$$\int_1^{1.5} \frac{1}{8}(4-t)\,dt.$$
The calculation for $\Pr(B)$ is similar.
c) Depends whether it is a working week or a full week. Let's say it is a full week. Let $T_1,T_2,\dots, T_7$ be the waiting times on the various days. We want $E(T_1+\cdots+T_7)$. By the linearity of expectation, this is $E(T_1)+\cdots+E(T_7)$.
We need $E(T_i)$. This is
$$\int_0^4 \frac{t}{8}(4-t)\,dt.$$
