1. Jul 27, 2017

### georg gill

I am looking for advanced problems in statistics with answer sheet on the subjects: probability distributions where you have to rewrite the sum of variables to a new probability distribution. Advanced problems in calculating variance and expected values for probability distributions. Advanced problems for bivariate problems. Does anyone know where to find this? If you know about a learning internet site who provides this please let me know where it is. But it is also nice if you have some problems that covers this in theory books if there is an answer sheet book that is also available.

PS: I have done some research myself and I found that studypug.com provided nice theory on probabilty of permutations and combinations etc. But on the subjects that I have adressed above I am more lost on finding subjects.

An example of an assignment is:

It is expecially assignments with difficulty as assignment c that I am looking for.

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2. Jul 27, 2017

### FactChecker

I have always been a big fan of the Schaum's Outline series of books because of the huge number of worked examples and exercises. And they are relatively cheap. I don't have one on probability, but there are a few to choose from.

3. Jul 27, 2017

### georg gill

I have downloaded a Schaum textbook. It was nice but unfortunately it did not have the problems I was looking for. Especially like the ones that requires rewriting between probability distributions as assignment c) in my first post. Anyone who knows about a problem book with answers that have thoose kind of problems?

4. Jul 27, 2017

### StoneTemplePython

I'm reading this as 'probability', more so than statistics. What level of 'advanced' are you looking for? Most of the time, adding or calculating expected values is quite easy. Variance, a bit less so. Convolving distributions, even less so (though if they give you the moment generating function maybe not so bad).

I would generally recommend using resources from MIT OCW like 6.041 and 6.262. However, I don't think they use the laplace distribution much and generally do not emphasize moment generating functions.

An alternative approach is Blitzstein's Intro to Probability Book. There are 600 + problems, a solution manual online with some solutions, accompanying video lectures on Youtube. Some of the problem solutions are available online -- if you wanted to jump right to them, you'd find them here:

https://projects.iq.harvard.edu/stat110/strategic-practice-problems

5. Jul 28, 2017

### georg gill

Thanks for the answer. I will look into both places and I have already found some assignments that I will work through. By what level of advanced I am looking for I would say that when it comes to rewriting functions they could have from normal difficulty to tough difficulty because then I can accumulate experience.