# Techniques for Proofs

• Feb 17th 2008, 03:14 PM
ShuxRei
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.

• Apr 3rd 2008, 07:03 PM
mr fantastic
Quote:

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.

• Apr 3rd 2008, 07:40 PM
awkward
You can find at least some of these results derived on the Planet Math website. For example, see

PlanetMath: binomial distribution
• Apr 4th 2008, 08:09 AM
ShuxRei
Quote:

Originally Posted by mr fantastic

We had tried google and wiki and all of those, but we couldn't find it.
• Apr 4th 2008, 12:27 PM
mathceleb
• Apr 5th 2008, 02:33 AM
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.
• Apr 5th 2008, 02:49 AM
mr fantastic
Quote:

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.
• Apr 5th 2008, 02:51 AM
ShuxRei
Quote:

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.
• Apr 5th 2008, 08:20 AM
mathceleb
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.