Recent content by waealu

Homework Statement Evaluate ∫^{∏}_{0}e(1+i)xdx Homework Equations I know that the Real part of this is -(1+e∏)/2 and the Imaginary part is (1+e∏)/2, but I can't get the right solution. I tried using u-substitution to create something that looked like ∫^{∏}_{0}((eu)/(1+i))du but I...

Hi, I have a quick question about variance. If you are trying to compute Var[3X-Y] where Var[X]=1 and Var[Y]=2, the correct formula is 32*Var[X] + Var[Y], but why do you add the variances of x and y? If you were computing Var[3X+Y] would it also be 32*Var[X] + Var[Y] ? Thanks, Erik

I understand that's how you could get the conditional variance, but how do you get the conditional expectation. Is it E[Y|X=x]=∫ y*f(y|x)*dy ? Where f(y|x) = f(x,y) / f(x) ?

Sorry, I think I posted this in the wrong part of the forum. I re-posted it in the Homework help section.

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it. If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution...

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it. If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution...

Homework Statement I am stuck on this problem relating to permutations: The first part asks how many ways can 6 people be lined up. This answer, I believe is 6! = 720 ways. The second part: If 3 specific persons, among 6, insist on following each other, how many ways are possible...

Nevermind, I was able to figure it out. They are looking for x=a*cos(\Theta)=a*cos(s/a) and y=a*sin(\Theta)=a*sin(s/a). Thanks, though.

For an assignment, I am supposed to find the parametric equation for the circle: x^2+y^2=a^2, using as a parameter the arc length, s, measured counterclockwise from the point (a,0) to the point (x,y). I understand that the parametric equation for a circle is x=a*cos(t) and y=a*sin(t), but...

Homework Statement Does the following series converge or diverge (use either the Limit Comparison or the Direct Comparison Test): \sum_{n=1}^{+\infty} \frac{3^{n-1}+1}{3^{n}} Homework Equations In a previous problem that was \sum_{n=1}^{+\infty} \frac{1}{3^{n-1}+1} I was able to...

Homework Statement I am supposed to find the value of the infinite series: \sum_{n=0}^{+\infty}\frac{\pi\cos(n)}{5^n} Homework Equations I asked this question before on this forum and micromass told me that I should use cos(n)=((e^i)^n+(e^(-i))^n)/2. That equation worked and I was...

Homework Statement (Sorry, but I haven't mastered using the sigma notation in these forums yet). Find the sum of the following infinite series: (n=0)^(inf) SIGMA ((pi)cos(n))/(5^n). Homework Equations I tried using the formula S=(a1)/(1-r). I know that a=pi, but I can't find "r."...

Okay, thanks. I figured it out now.

Homework Statement The problem asks to integrate dx\(sqrt(abs(x-1))) from 0 to 2. \int(dx/(sqrt(abs(x-1)))) Homework Equations I had the limit as b approaches 1 of the integral (from 0 to b) plus the limit as c approaches 1 of the integral (from c to 2). The Attempt at a Solution...

Homework Statement If g(1)=3, g(5)=8 and the integral from 1 to 5 of g(x)dx=-9. Then, evaluate the integral from 1 to 5 of xg'(x)dx. 2. Homework Equations and attempt at solution I used integration by parts to get =xg(x)-(integral of)g(x)dx from 1 to 5. Then substituting in, I get...