Recent content by wtmoore

I am still unsure. Take L() to be notation for laplace. Top line, L(X')=sx(s)-X(0) L(Y')=sy(s)-Y(0) L(Y)=y(s) L(Z)=z(s) How do I solve from here? sx(s)-X(0)+sy(s)-Y(0)=y(s)+z(s)

Homework Statement Here's the question: Use laplace transforms to find X(t), Y(t) and Z(t) given that: X'+Y'=Y+Z Y'+Z'=X+Z X'+Z'=X+Y subject to the boundary conditions X(0)=2, Y(0)=-3,Z(0)=1. Now I have learned the basics of laplace transforms, but have not seen a question in...

Homework Statement I have taken a random sample such that X~N(8,2). I want to use the samples that I have generated to estimate E(xbar), E(s2), E(α21) and E(α22) for the population. Homework Equations The Attempt at a Solution I am not entirely sure how to do these. I know that for a...

I can, but it's not homework, it is revision for exams, they are extra problems we can choose to do which will help us in exams. The question is stated as it is, but instead of saying I wish to find, it says, find, I haven't left any information out, and have asked it in the first person...

It's a tutorial question for a class I'm taking. It's basically revision, I will write out the formulas for the two sigmas. My understanding was they they were the population variances, but, I meant to say that the sigmas have hats on them for estimated, so I think they are sample variances that...

I have created 1000 random samples of size 10, where X~N(8,2). For each sample I have calculated the sample mean, sample variance, (sigma1)2 and (sigma2)2. I want to find a 95% confidence interval for the mean assuming the population variance is known, and a 95% confidence interval for the...

Homework Statement I'm trying to find the Laplace transform of tJ''0(t), it's from bessels equation, but that doesn't matter too much at the moment, I just need to integrate (e^-st)*t*J''0(t) but am unsure how to go about this with the J''0(t) in there.

I realize now, I messed up the integration. The general solution is: y=-x/(ln(Ax^2))

[Ok so I have transformed a 1st order homogenous ODE into a seperable ODE. However I am having trouble seperating to get y on it's own. Here's the problem: du/dx=(2u^2)/x where u = y/x du/(2u^2)=dx/x <<can't get tex to work -1/(4u^2)=ln(x)+C=ln(Ax) <<can't get tex to work...

thanks dick

Ok, so now the general solution is: T=Cexp(-kt)+T0 particular solution is T=70exp(-kt)+30 when T=100 when t=0 and T0=30 However for the next bit I don't understand, Am I doing T(15)=70? Does this give T=Cexp(-15k)+30? So 70=70exp(-15k)+30 k=0.0373 Then T=40 40=70exp(-0.0373t)+30...

Homework Statement Question According to Newton’s Law of Cooling, the rate at which a substance cools in air is proportional to the difference between the temperature of the substance and that of air. The differential equation is given byAccording to Newton’s Law of Cooling, the rate at which...

Yeh I was thinking just at the end not the fact that they are going to multiply each other. Thanks for all your help Jbunnii

Thanks jbunniii, I understand all of it, and have managed to complete 2 similar questions now. My only question is, why is it the square root? Surely if <f,f> = pi/2 then we need 2/pi to make this 1?

Yeh I tried these, acos(0)+bsin(0)=0 Then a must be 0. acos(pi/2)+bsin(pi/2)=0 then b must be 0. Is it enough to write this, or is there some sort of other form I can generalize it for?