Recent content by TeenieBopper

Yes, I realized today that YY' is a singular matrix, making it impossible to find the inverse. as soon as you said 'quadratic form' I remembered something from the notes (I didn't recognize it as quadratic form because I don't remember learning about them in my linear algebra course. Anyways...

I asked this question here, however the title of the thread (and the thread itself) was sloppy and unclear.I could not find a way to delete or edit. This is for a regression analysis course, and I've only taken one introductory course on linear algebra, so when I Google'd "finding a symmetric...

It's an absolute value function, so if I graph it, it's essentially two triangles, each with a point at 0,0 and then vertical edges at x=-2 and x=2. So there's two cases, -2<x<0 and 0<x<2, that I look at seperately. Looking at the first case, the integral is $$\int_{-2}^{x} \frac{-t}{4} dt =...

I changed the pdf so it should be technically correct now So, because it's an absolute value function, it should be: $$\int_{-2}^{x}\frac{-x}{4} dt + \int_{0}^{x}\frac{x}{4}dt$$? Because then I get $$F(x) = \frac{x^2}{4} - \frac{1}{2}$$ which again, isn't monotone increasing. Ultimately, my...

Homework Statement Find the CDF of f(x) = |\frac{x}{4}| if -2<x<2 \\ 0 otherwise Homework Equations The Attempt at a Solution I have to integrate the pdf and to do so, I have to split it into two parts \int_{-x}^{0}\frac{-t}{4}dt + \int_{0}{x}\frac{t}{4}dt integrating I get \frac{x^2}{8} +...

Ah, I see. I was just using the buttons at the top and side. Hopefully I'll get this right this time. The original equation. \frac{1}{n-1} \sum_{i=1}^n (Y_i - \bar{Y})^2 = \frac{1}{n(n-1)}\sum_{i=1}^{n-1} \sum_{j=i+1}^n (Y_i-Y_j)^2 Like I said, the (n-1) from both sides cancel, and...

Homework Statement Showthe two forms of the sample variance are equivalent: \frac{1}{n-1}\sum_{i=1}^\n (Yi-Ybar)2 = \frac{1}{n(n-1)}\sum_{i=1}^\n \sum_{j>i}\n (Yi-Yj)2 The first summation is from i=1 to n, the second is i=1 to n and the third is j>i to n. Sorry, I don't know how to format...

Well, the solution with the eugenol products was clear, and the FeCl_3 was yellow, and when we mixed the two, the solution was yellow. I just assumed that it was because of the FeCl_3. Yeah, this was why I was confused, because we didn't explicitly add a halogen. I did some more reading, and...

Homework Statement Complete the following reactions, giving the correct structure for each organic product: eugenol + FeCl_3 -> eugenol acetate + FeCl_3 -> Homework Equations The Attempt at a Solution When I did this lab, my partner and I didn't notice a reaction when we...

I have two questions involving lines and planes. They're both fairly simple, but I'm stuck. I'm sure someone is going to point something out and it's going to make me smack my forehead. Homework Statement Where does the line through*(1, 0, 1) and (4,*−2,*4) intersect the...

Homework Statement Suppose r>1. Prove the sequence \sqrt[n]{1 + r^{n}} converges and find its limit. Homework Equations The Attempt at a Solution It's obvious that the sequence converges to r, so I know where I need to end up. My first instinct is to use the squeeze theorem...

Homework Statement Prove \sum\frac{(-1)^k}{k^2} is a Cauchy sequence. Homework Equations Definition of Cauchy sequence: |a_{n} - a_{m}|<ε for all n,m>=N, n>m The Attempt at a Solution I thought if I could prove that the above summation was less than the summation of 1/k^2, the...

Yes, sorry. Assume that an and bn converge to a and b, respectively.

Homework Statement Use the fact that an= a + (an - a) and bn= b + (bn - b) to establish the equality an*bn - ab = (an-a)(bn-b)+b(an-a)+a(bn-b). Then, use this equality to prove that the sequence {an*bn} converges to ab. Homework Equations Definition of convergence: |an*bn - ab| < ε...

Homework Statement Calculate the molar solubility of Cu(OH)2, Ksp = 2.2 × 10^–20, in 0.87 M NH3. Don't forget to use the complexation reaction Cu2+ + 4 NH3 ⇌ Cu(NH3)42+, K = 5.0 × 10^13. Homework Equations Ksp=[A]^m[B]^n Keq=[product]/[reactants] The Attempt at a Solution I...