Hi Ray, thanks for your answer.
You are correct, I forgot the "small" little detail that we generated it from a uniform distribution. I think/thought I knew what a density function is, and that the probability function for a uniform distribution is 1/(b-a+1). I can't udnerstand what the...
Homework Statement
We have an interval [0,1], which we divide into k equally sized subintervals and generate n observations. Let's call the number of observations which falls into interval k_i, X_i. What distribution does X_1 have?
Now we define Y_i=X_i/n. Derive the Expected value...
I meant the column vectorspace, the range yes! I mixed up E and I, we use E for the identity matrix.
So, what we've done here is(if you could check if my line of thoughts is correct), made the transformation for an arbitrary matrix A and X. Examined the nullspace by setting AX=XA, and shown...
Hi. Define a linear mapping F: M2-->M2 by F(X)=AX-XA for a matrix A, and find a basis for the nullspace and the vectorspace(not sure if this is the term in english). Then I want to show that dim N(F)=dim V(F)=2 for all A, A≠λI, for some real λ. F(A)=F(E)=0, so A and E belongs to the nullspace...
In polar coordinates it would be r^2-2rcosθ=0 ⇔ r=2cosθ. So it will go from 2cosθ and follow the sphere upwards... nah I am having a hard time visualizing it :(
Yes, the answer is probably a small typo then.
Hi, thanks for answering. This was kinda the vision I had, tho i was unfamiliar with cylindrical coordinates. I don't understand where cos(θ) comes from in the integrand? The jacobian from the substitution would just be r, no? Or have I missed something fundamental here? The double integral gets...
Homework Statement
Find the volume of the object, defined by these inequalities(?): x^2+y^2+z^2≤4, (x-1)^2+y^2≥1, (x+1)^2+y^2≥1Homework Equations
The Attempt at a Solution
First we draw the object, and realize that it's a sphere with 2 circles in it with radius 1 at (-1,0) and (1,0). Our...
Thx! I need to get the picture of this straight in my head, after I've sorted the picture out I have no problems calculating it. Is it correct if I think of it this way?
At first we have the circle, let's call it D, at (1/2,0) with r=1/2. We make the substitution and move into (0,0). We have...
Hi Vargo, thanks for answering!
I understand that this means that θ varies from -π/2 to π/2, which is the correct answer. Tho I don't understand why it does. I probably don't understand the mapping fully, I think of E as some rectangle in some r,θ-plane, and I don't understand why we look at...
Homework Statement
I have the double integral,
∫∫sqrt(x^2+y^2) dxdy, and the area D:((x,y);(x^2+y^2)≤ x)
Homework Equations
The Attempt at a Solution
By completing the squares in D we get that D is a circle with origo at (1/2,0), and radius 1/2. Then I tried changing...