how to correct wikipedia edit error?

Originally posted by humy
I have now carefully edited all the changes in:

http://en.wikipedia.org/wiki/Probability_density_function

All the changes I made are in the "Example" section only.
Does everyone approve?
The main change there I made is replace where it previously said:

"Instead we might ask: What is the probability that the bacterium dies between 5 hours and 5.01 ho ...[text shortened]... illion nanosecond in a second, is (2 hour−1)×(1 nanosecond) = 2 × 10−9 / 3600 ≃ 5.556×10−13...."

I have just noticed that someone that calls himself Sbyrnes321 has reedited (not undo ) and enhanced some of my changes I made there to make them even better -good for him!

I knew my verbal skills are not as good as some peoples and I appreciate it when someone with obviously much better verbal skills than I helps me out with the wording.

He made it shorter and more to the point (close to halving the number of words! ) -something I find hard to do because one of my deficiencies is I always find it extremely difficult to verbally summarize things -don't know why. It certainly isn't due to lack of effort or motivation. Perhaps my (mild ) dyslexia is to blame for that?

Originally posted by humy
On an unrelated maths problem (although still to do with probability ) :

Is there a way of simplifying the RHS expression in the equation:

y = ( x ^ n ) * ( ( 1 – x ) ^ ( e – n ) )

?

( don't know if this has any relevance but, for the application I have in mind, both n and e are natural numbers while x is a continuous random variable in the [0, 1] ...[text shortened]... ssible probabilities! )

I am trying to make it a bit easier for myself to finds its integral.

You might have to find a numerical approach for each n & e... there doesn't seem to be any worthwhile rearrangements to aid in the integration of the function in general.

Originally posted by joe shmo
You might have to find a numerical approach for each n & e... there doesn't seem to be any worthwhile rearrangements to aid in the integration of the function in general.

Thanks for that.

With both e and n being natural numbers, I think I have found its integral which I think is:

definite integral of ( x ^ n ) * ( ( 1 – x ) ^ ( e – n ) ) dx from x=0 to x=1

= ( n! * ( e - n )! ) / ( e + 1 )!

I hope that is right. Can anyone confirm?

This would be fine for small/modest n and small/modest e but, for very large n or e, because it is too difficult to compute massively large factorials (my calculator can only find the factorial for whole numbers less that 70 ), I guess this formula would be impractical and I would have to use a numerical approach -unless someone can give me a formula for an approximation of the integral from x=0 to x=1 for very large n or e but avoids the factorial function?
Anyone?

Originally posted by humy
Thanks for that.

With both e and n being natural numbers, I think I have found its integral which I think is:

integral of ( x ^ n ) * ( ( 1 – x ) ^ ( e – n ) ) dx from x=0 to x=1

= ( n! * ( e - n )! ) / ( e + 1 )!

I hope that is right. Can anyone confirm?

This would be fine for small/modest n and small/modest e but, for very large n or e, b ...[text shortened]... e formula for an approximation of the integral from x=0 to x=1 for very large n or e ?
Anyone?

How did you come to find your result for the integral?

As far as I can tell, no elementary function has ( x ^ n ) * ( ( 1 – x ) ^ ( e – n ) ) as its derivative?

To check the result, what would help is the function in "x" before the integration (x=0 to 1) you performed?

Intuitively, I have to say the result is incorrect.

Originally posted by joe shmo
How did you come to find your result for the integral?

I kind of 'cheated' by searching the net and finding the integration to a formula with the same structure although the letters used are all different:

http://math.stackexchange.com/questions/122296/how-to-evaluate-this-integral-relating-to-binomial

in this case, for the particular application I have in mind, I am only interested in the area under the curve from x=0 to x=1

Originally posted by humy
I kind of 'cheated' by searching the net and finding the integration to a formula with the same structure although the letters used are all different:

http://math.stackexchange.com/questions/122296/how-to-evaluate-this-integral-relating-to-binomial

in this case, for the particular application I have in mind, I am only interested in the area under the curve from x=0 to x=1

Ok...

I guess I don't have good intuitions about non elementary functions. (Apparently its the Beta Function)

Originally posted by joe shmo
(Apparently its the Beta Function)

Thanks for telling me that. I just looked that up at:
http://en.wikipedia.org/wiki/Beta_function
and now I must gradually mull over it so I can understand it properly.
But, unless I am missing something, it doesn't appear to me to be exactly the same function but rather a similar function.
I haven't yet worked out how it relates to my formula if it relates at all!

looks like I may have to also study:
http://en.wikipedia.org/wiki/Beta_distribution