1. ## Techniques for Proofs

Hi.

My teacher is a bit crazy. And I'm having a lot of trouble with something he assigned us.

Okay, basically, we have to make a chart of all the discrete distributions, their canonical problems, their p.m.f.'s, means (E(X)), and variances, which the formulas and answers for all of those are in our book.

However, he also wants us to provide a verification technique on how to prove these formulas. I've looked in the book and there was nothing, and we've only gone over a few in class. This was assigned on the last class period and is due before the next class, so I'm really stuck and don't know where to go.

I work tonight and have class pretty much all day tomorrow, so I can't seek help elsewhere. Does anyone know of a good website or something where I can find this information? The distributions I have to "prove" are: Bernoulli, Binomial, Geometric, Hypergeometric, Negative Binomial, Poisson, and Uniform.

2. Originally Posted by ShuxRei
Hi.

My teacher is a bit crazy. And I'm having a lot of trouble with something he assigned us.

Okay, basically, we have to make a chart of all the discrete distributions, their canonical problems, their p.m.f.'s, means (E(X)), and variances, which the formulas and answers for all of those are in our book.

However, he also wants us to provide a verification technique on how to prove these formulas. I've looked in the book and there was nothing, and we've only gone over a few in class. This was assigned on the last class period and is due before the next class, so I'm really stuck and don't know where to go.

I work tonight and have class pretty much all day tomorrow, so I can't seek help elsewhere. Does anyone know of a good website or something where I can find this information? The distributions I have to "prove" are: Bernoulli, Binomial, Geometric, Hypergeometric, Negative Binomial, Poisson, and Uniform.

3. You can find at least some of these results derived on the Planet Math website. For example, see

PlanetMath: binomial distribution

4. Originally Posted by mr fantastic
We had tried google and wiki and all of those, but we couldn't find it.

5. Thank you. We found those, but they fail to provide proofs. We also had to find the techniques to prove the pmf was equal to 1, etc... which is the part we were having trouble with. We couldn't find or write proofs.

6. Originally Posted by ShuxRei
Thank you. We found those, but they fail to provide proofs. We also had to find the techniques to prove the pmf was equal to 1, etc... which is the part we were having trouble with. We couldn't find or write proofs.
Well, if you know the moment generating function for these distributions, finding the mean and variance is simple.

If you search the math help forum:

moment generating function

you'll find the derivation of the moment generating function for many of these distributions.

7. Originally Posted by mr fantastic
Well, if you know the moment generating function for these distributions, finding the mean and variance is simple.

If you search the math help forum:

moment generating function

you'll find the derivation of the moment generating function for many of these distributions.
Thank you.

8. Ok, I see what you mean.

Binomial Distribution -- from Wolfram MathWorld

This shows the derviation of the different moments as well as other helpful items.