Consider the continuous random variable T=' waiting time at the bus station'. Assume a max delay of 30 minutes. Answer the following questions:
a. Determine the sample space S associated with the random variable T;
b. given the function f(t)=A*t, with t time in minutes, find the parameter A such that f(t) is the probability density of T, that is f(t)*dt=Pr[ tc. derive the mean and standard deviation of T;
d. compute the probability that T>15 minutes;
e. compute the probability that T<3 minutes.
f. Compute the probability that T=15 minutes.