Preparing for First Midterm: How Can I Catch Up?

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In summary, the conversation revolved around a problem involving calculating the distribution function of a density and taking the limit as e approaches 0. There was a discussion about using the fact that g is continuous and how the integral would change based on the form of f_e. Ultimately, it was suggested to change the limits to only include the non-zero region of f_e.
  • #1
Shackleford
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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
 
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  • #2
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
 
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  • #3
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.
 
  • #4
lanedance said:
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."
 
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  • #5
[tex] \lim_{\epsilon \to 0} \int_{-\infty}^{-\infty} dx g(x) f_{\epsilon}(x-a) [/tex]

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
 

Related to Preparing for First Midterm: How Can I Catch Up?

1. How much time should I spend studying for the first midterm?

The amount of time you spend studying will vary depending on your individual learning style and the difficulty of the material. It is recommended to start studying at least a week in advance and spend a couple of hours each day reviewing and practicing the material.

2. What study strategies are most effective for catching up on material?

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Prioritize studying the material that you are least confident in or that you struggled with in class. It is also important to focus on key concepts and main ideas rather than trying to memorize every detail.

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This depends on your personal preference. Some people find it helpful to study alone so they can focus and go at their own pace, while others may benefit from studying with a group for additional support and discussion. You can also try a combination of both methods.

5. What should I do if I am still struggling after studying?

If you are still struggling after studying, it may be helpful to reach out to your professor or TA for clarification on specific topics. You can also form a study group with classmates to review the material together and ask each other questions. Additionally, try to stay calm and focused during the exam and don't be afraid to skip a question and come back to it later if you need more time to think.

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