Not sure why, but it's not letting me edit the first post.
It should be kx^(b-1) *exp(-ax^b) not ∫kx^(b-a) *exp(-ax^b), but anyway, I took another crack at it and I solved it!
u = ax^b
du = abx^(b-1) dx
∫kx^(b-1) *exp(-ax^b) dx
= k/(ab)∫exp(-u) du
= k/ab[1] = 1, so k = ab.
∫kx^(b)...
Homework Statement
This is the full question, but we're only asked to do b.
A random variable x has a Weibull Distribution if and only if its probability density is given by f(x) = {kx^(b-a) *exp(-ax^b) for x > 0 }
where a and b > 0.
a) Express k in terms of a and b.
b) Show that u = a^(-1/b)...
Definitely missed that completely.
Thanks a lot. It's amazing how the simplest things can sometimes give you so much trouble.
Just to make sure I'm understanding it correctly, the U 1 to infinite of (0,n) is saying you're doing a union of {0, .. Real Values, .., 1} U {0, .., 2} U {0,..,3}...
Homework Statement
I'm reading through the introductory pages of my real analysis book and for some reason I can't wrap my head around this seemingly simple concept. The book is talking about collections of sets and something new to me called the "index set".
I apologize ahead of time...
To be clear, you're saying that you can't just simplify (a^i)^i to a^(i^2), BUT i^i does have infinite different values, correct?
This is starting to boggle my mind a little bit. I can't seem to wrap my head around it.
I'm reading the wikipedia page...
Can someone explain if this is true or if there's anything wrong with the following logic?
e^ix = cos(x) + isin(x)
Let x = pi/2 + 2npi
Then,
e^ix = i
Take both sides to the exponent i,
e^-x = i^i
e^-(pi/2 + 2npi) = i^i
But, e^(pi/2 + 2npi) has infinite different values.
I've been looking...
Thanks for the help :).
I now understand where they get the sin(x) + rsin(x) in the numerator, and where the 1 + r^2 comes from in the denominator. However, how do they get the 2rcos(2x) in the denominator?
EDIT: Never mind, I figured it out.
I forgot about cos(x) = 1/2(e^ix + e^-ix)...
Homework Statement
http://www-thphys.physics.ox.ac.uk/people/JamesBinney/complex.pdf
Example 1.2 (Page 6)
Homework Equations
De Moivre's Theorem, Euler's Formula, and other simple complex number theory formulas
The Attempt at a Solution
I'm having troubles understanding the format, which...
They're just asking which are subspaces of R^n.
So you have to show:
a) cV, where V is a subset of the subspace, is an element of the subspace.
and b) v + w, where v,w are elements of the subspace, is again in the subspace.
It also wants to know what the domain of the subspace is from what I...
It's D=fxx(fyy)-(fxfy)^2
If d > 0,
and fxx > 0, it's a local minimum or
fxx < 0, it's a local maximum
if d < 0,
then it's a saddle point.
However, you can't use this for this function as it's a function in terms of one variable.
So,
r=(1-x)(1+x)
= 1 - x^2
Which is a...
You have to prove:
a) It's linearly independent:
If S spans, that means ...
None of the vectors in S are a linear combination of another.
How can you prove this?
Think ..
av1 + bv2 + cv3 .. + Lvn = 0, implies a,b,c .. L = 0.
b): It spans.
If S spans V, that means that any vector of V...