Preparing for First Midterm: How Can I Catch Up?

[Shackleford]

Not exactly sure how to do (a) and (b). Do I need to calculate the distribution function of this density?

My first midterm got moved up to this Thursday. Unfortunately, I'm a bit behind in this class. I don't think I'm going to be able to adequately cover all of the material in time.

http://i111.photobucket.com/albums/n149/camarolt4z28/untitled.jpg?t=1299629377

http://i111.photobucket.com/albums/n149/camarolt4z28/1-1.jpg?t=1299629328

 

[lanedance]

think about what happens to f as e gets small, it becomes very narrow and integrates to 1, tending towards a delta function, try to write out the form of the integral such that you can take the limit and use the fact g is continuous

 

[HallsofIvy]

No part of that problem says anything about a "pdf" or any probability- it just asks about an integration. And, I suspect that how you do it will depend strongly upon what "f" is which we are told was given in a previous problem.

 

[Shackleford]

think about what happens to f as e gets small, it becomes very narrow and integrates to 1, tending towards a delta function, try to write out the form of the integral such that you can take the limit and use the fact g is continuous

It goes to infinity but still integrates to one because it should integrate to the distribution function value limit, which is one? Do I change the limits from -1 to 0?

I know the derivative of the Heaviside function is the Dirac Delta "function."

 

[lanedance]

\lim_{\epsilon \to 0} \int_{-\infty}^{-\infty} dx g(x) f_{\epsilon}(x-a)

as suggested substitute in the form of f_e, clearly anywhere f_e is zero does not change the integral so you can change the limits to be only the non-zero region of f_e