a)
In this problem, I'd say that the answer is a/2. The main issue is that we have to prove that. Basically, what we need to deal with in this problem is that PDF(probability density function). Use |x-a| and PDF. Also Integrate. And that's all. I cannot write the process of this demonstration due to the limited environment to draw integral. I know I'm just lazy to type a whole bunch of mathematics formulas.
b)
It looks like no way to solve one because it is totally different situation in Problem a). In this case, it is sure that we have to utilize the exponential random variable method. However, if you thought it was going to be complicated, you would miss the point. Just time the exponential part by |x-a| and integrate them. For example, when the lamda is 'S', the equation that you should integrate will be S*e^(-sx)*|x-a|. That integral calculation might be tough one, but it would not be a big deal. (If you are not idiot, you know that you should distinguish two equations between when X>a and when X<a.
Also one more new I gonna tell you guys is that:
This homework 5 will be exponentially difficult homework ever. Even our TA agreed the fact that this assignment was not easy. I will cross the finger. Good luck guys.
One more thing.
I want to cry.......T_T I still got to finish four more problems. Thank you Professor.
