Recent content by vincentvance

With X having the exponential $(\lambda)$ distribution and $Y = X^3$, how do I compute the joint cumulative distribution function? Here is how far I've come: $F(x,y) = P(X ≤ x, Y ≤ y) = P(X ≤ x, x^3 ≤ y) = P(X ≤ x, X ≤ y^{1/3}) = P(X ≤ min(x, y^{1/3})$, $f_x(x) = \lambda e^{-\lambda x}$$ for...

Oh, I actually think I get it now. Thank you for your patience!

Thank you! In the post you linked it says "Some caution is to be adopted using the table 2.1 because the $w_n$ are valid only if the sequences themselves aren’t solution of the homogeneous DE and if that is the case a different procedure must be adopted." Isn't the sequence a solution to the...

Hi, I have a question about how to find the particular solutions when trying to solve recurrence relations. For example, trying to solve an+2 = -4an + 8n2n , I begin with finding the roots in the characteristic polynomial associated with the homogeneous equation, so r1 = 2i and r2 = -2i...

Ah. Of course, now it makes sense. Thank you so much!

I feel like such an idiot, but I don't understand why for example if x ≡ 5 (mod 6) then x ≡ 2 (mod 3).

Hello, I am trying to prove that the system x ≡ 5 (mod 6) x ≡ 7 (mod 15) has no solution. This example is done in my textbook and they say one should first assume that there is a solution x, and that when taking classes mod 6 the second equation implies that 2x ≡ 2 (mod 6). After this the...

Hi, I'm trying to solve this problem and I'm stuck. What I want to do is determine the kind of surface from this equation: x2-2y2-3z2-4xy-2xz-6yz = 11 Matrix representation: 1 -2 -1 -2 -2 -3 -1 -3 -3 I want to find the eigenvalues so I write the characteristic equation like...