Thanks a lot for the replies. I looked through a couple of books but they only talked about multiple variable regression in too vague manner. This'll help me get forward. Thanks again.
Hey!
I'm working with some regression related stuff at the moment and i'd need some help with multiple variable prediction interval. Prediction interval for a single variable can be calculated using
PI = \hat{\beta_0}+\hat{\beta_1}x_i \pm t^* s_e \sqrt{1+\frac{1}{n} +...
I'm somewhat familiar with the laplace transform and thus had it a go.
I'll use "k" to replace that nu mark for the sake of convenience.
Now \frac{\partial f(v,t)}{\partial t} + a \cdot \nabla_v f(v,t) = -k (f(v,t) - f_0(v)).
What was probably clear before but what i didn't state, was that...
Homework Statement
Solve the Boltzmann equation for a homogeneous plasma with not external forces present when the collision term is
\frac{\partial f(v,t)}{\partial t} = -\nu (f(v,t) - f_0(v)),
where \nu and f_0 are constants.
Homework Equations
Boltzmann equation
\frac{\partial...
Homework Statement
Dice is thrown 6 times. What's the probability of numbers 5 and 6 showing up at least once.Homework Equations
This ought to be basic probability calculus but i just can't get my head around this. Some kind of attempt(ish) below. THe answer ought to be 0.418 or 41.8%.The...
I'm actually starting to wonder whether it might be a typo by my professor.
Since it seems the function would only get one value if defined the way i stated in the original post. \frac{1}{n} right?... or?
Right, I gave it a wild shot and this is what i came up with.
The upper sum is defined as
\sum_{k=1}^{n}(x_{k+1}-x_k)*sup(f(x))
Now let's choose such width for the Riemann sum quadrilateral that
0.5*(\frac{1}{n} - \frac{1}{n+1})= \frac{1}{2n(n+1)} = r_n.
Lets place each quadrilateral...
It actually is f(x)=\frac{1}{n}. Yea, I'm trying to approach this with Riemann sums and the intervals don't need to be equal in size as far as i understand.
Let f:[0,1]->ℝ and f(x) = \frac{1}{n} when x=\frac{1}{n²}, n=1,2,... and 0 in other case.
Define such spacing/interval D that S_D-s_D < \frac{1}{100}. Here S_D refers to the upper sum and s_D the the lower sum.Now, I'm not sure how to approach this really since the sum is defined so that the...
1. Prove that 0 is an upper bound of S=\{x\in \mathbb{R}|x<0\}. (OK, this step is trivial).
2. Prove that S=sup\{x\in \mathbb{R}|x<0\}\leq 0. (Also kind of trivial, if you think of what a supremum is).
3. Prove that S=sup\{x\in \mathbb{R}|x<0\}\geq -\epsilon for all \epsilon>0.
1)
0 is an...
Righty, here we go again.
We want to prove that for all ε>0, sup(d(x,y))>2r-ε.
Let \epsilon>0 be arbitrary.
Antithesis: sup(d(x,y)) \leq 2r-\epsilon
This means that 2r-\epsilon is an upper bound of the set.
Let \epsilon>\delta>0. Now 2r-\epsilon<2r-\delta<2r which means 2r-\epsilon cannot...