Statistics this time.
I have a poisson distribution, and I am just trying to work out my degrees of freedom.
I have 7 columns of data. I have the mean. I have not worked out the variance yet. But I do have the total frequency.
So does the total expected frequency count as a constraint
In other words, is my degree of freedom 7-1=6 or 7-2=5
(it does make a difference because 7-1 means that it is a poisson distribution and 7-2 means it isn't)
So then l-x=l-[4l/(pi+4)]
Is that the answer? That's the minimum right? How do I find the max? I imagine it is just using the whole length of rope for a circle, but how to I prove that? I can prove that a circle and a square of a set perimeter, the circle will have the biggest area.
A piece of string of length L is to be cut into two pieces. One piece is formed into a square, the other into a circle.
a)Where, if anywhere, would the string be cut to that the total area of the two shapes is a small as possible
Where, if anywhere, should the string be cut so the area is as large as possible
This is what I have:
I'm assuming that the maximum would be just a circle, but I don't know how I'd show that. And not sure how I'd do the minimum
By using the Substitution u=cot theta or otherwise, find the integral of cot ^4 theta d theta
My teacher says there is a really simple way to do this, so it shouldn't take hours.
He also gave us a hint of writing down sec^3 theta and tan theta, but I can't see how we can get to that.
Okay. so the first thing I need to do is find A and B as shown above?
Then, how do I integrate the fraction. My teacher said it was something to do with Partial Fractions, and did say if i couldn't do the question not to worry because I've not studied partial fractions before, but I would like to at least understand how the answer is derived.