Physics Lord

Follow me in my adventures in the world of physics!

[physicslord-blog]

Student: Let me get this straight.

Student: You gave us this homework assignment a week ago, but didn't give us the equations we needed to solve the problems until today.

Student: WHY.

Professor: It gives you more XP.

[physicslord-blog]

Student: Why don’t we hear about Quantum Mechanics outside of classes, like in the media or the news?

Chemistry professor: Well, the math usually makes most people crap their pants.

[physicslord-blog]

MGF and the binomial distribution

The moment generating function M(t), can give us the different moment of a distribution and it’s sometimes more easy to compute mean and variance this way. 

I propose to show how to do it with the binomial distribution. We can describe the binomial distribution this way:

This distribution describe the probability of an event to occure x times in n tests. It’s not so useful in physics, but it help to introduce the Poisson and normal distribution which are very important in physics and mathematics.

If we compute the MGF we get this result:

This is not a function to complicated to derive and that’s fun, because we are going to devide it two times.

To get the nth moment of the binomial distribution, we only need to let t=0 in the nth derivative of the MGF. Wcan compute the mean just to be sure this is true.

This is useful and so why not trying to compute the variance this way?

This is a useful function and as we see it give good results really fast. Even if I didn’t show as a proof that it work, we can still appreciate how it work his case. If you want to see a proof of this function I’m probably sure google can help.

My source for this was the book A first course in probability of Sheldon M. Ross or in french, Initiation aux probabilités.

[mathprofessorquotes]

The variables on this side are the nice animals, and the ones here are the evil animals.

Abstract algebra professor (via mathprofessorquotes)

[physicslord-blog]

[elegantproof]

This math book is pretty ambitious

[nemfrog]

Diffraction patterns _Crystals & X-Rays_ 1970

[mathprofessorquotes]

Don’t be afraid engineers. Once, a textile engineer was here trying to be physicist. That was hard for him, but now he’s an expert in superstrings!

Physics professor (via mathprofessorquotes)

[scienceprofessorquotes]

What does a subatomic duck say? Quark.

Physical chemistry professor (via scienceprofessorquotes)

[mathprofessorquotes]

Torque. Not twerk. But we can talk about both if you want.

Physics teacher (via mathprofessorquotes)

[physicslord-blog]

Cyclops numbers

I know this isnt physics, so everyone is going to be sad, but this is in fact a very cool math fact!

To get more informations about such numbers, you can always use google or see the video of numberphile about it!

[lthmath]

The concept of powers was known to the old Babylonians and Egyptians; in the Rhind Papyrus, Ahmes the Scribe used a word meaning mass or quantity to denote the unknown quantity the we call x.

In the days of rhetorical mathematics, powers of unknown had to have names before they could be described by symbols. The ancient Greeks, to whom mathematics meant geometry, called the square of the unknown a tetragon number, that is, a four-corner number.

Diophantos of Alexandria used the word “power” for the square of the unknown; the third power was a “cube”; the fourth, a “power-power”; the fifth, a “power-cube”; and the sixth, a “cube-cube”.

The first algebraic power symbols corresponding to our x^2, x^3, x^4, etc., to appear in print were found in the “Arithmetica integra” by the German mathematician Michael Stifel.

[a-gay-teenager-deactivated20190]

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[physicslord-blog]

My favorite problem can be solve with this one!