Recent content by dvvv

I just used it to confirm I was right. Thanks for your help.

Tried again and got: ((3 w^2 - 2 w + 1) σ^2)/(2 n) which is correct according to wolfram alpha http://www.wolframalpha.com/input/?i=w%5E2%28%CF%83%5E2%2Fn%29%2B%281-w%29%5E2%28%CF%83%5E2%2F2n%29 What now?

I guess it would be (σ^2)/10 and (σ^2)/20, so it's (σ^2)/n and (σ^2)/2n for \bar{X}_1 and \bar{X}_2, respectively. I subbed that into \text{Var}(a \bar{X}_1 + b \bar{X}_2) = a^2 \text{Var}(\bar{X}_1) + b^2 \text{Var}(\bar{X}_2) and subbed in a and b, and I got (σ^2(w^2+1))/2n I still...

I don't know why I did that either. So is it right to say: \text{Var}( \bar{X}_1) = \text{Var}(\bar{X}_2) = σ^2/n ? How do I work out what w is?

Homework Statement Let \bar{X}1 and \bar{X}2 be the means of two independent samples of sizes n and 2n from an infinite population that has mean μ and variance σ^2 > 0. For what value of w is w\bar{X}1 + (1 - w)\bar{X}2 the minimum variance unbiased estimator of μ? (a) 0 (b) 1/3 (c) 1/2 (d) 2/3...

I think I would substitute x=e^rt. I did that on another question. I'm probably wrong. It's too late for me to learn all this now. Thanks anyway!

Homework Statement Solve the following second order linear differential equation d2x/dt2 + x = 2 cos(t) subject to the initial condition x(0) = 0 and dx/dt (0) = 0. What type of motion do you find? Homework Equations The Attempt at a Solution I don't know where to start

OK. I keep making stupid mistakes. Thanks for all your help.

x = (2x' - y')/14 y = y'/2 Sub'd in and got x' + 3y' = 14

x = (-2x' + y')/7 y = 3x' + y' I substituted that into x+y=2 and I got 19x' + 8y' = 14 edit: made a mistake,..one sec

For the last part I did SoT(x,y) = \left[ \begin{array}{cc} 7 & 10 \\ 0 & 2 \end{array} \right] \left[\begin{array}{cc} x \\ y \end{array} \right] and I got (7x+10y, 2y). I substituted that into x+y=2 and I got 7x + 12y = 2. Is that right?

Yeah sorry about that.

Oh well I thought I was getting SoT but I got confused apparently. I get it now. SoT is 7 4 0 -2 edit: made a mistake, I'll fix it in a second.

I got 12 10 -5 -3 I just multiplied T by S. I wasn't sure what to do since it's just ToS not ToS(x,y) or something like that.

Well I can't seem to find any definition, but if you had ToS(u), that would be equal to T(S(u)). Similarly SoT(u) would be S(T(u)) I assume.