So I have a couple problems I'm working on, for homework. I was hoping I could get a little guidance as to where I should go next. First problem, the one I have the least idea on: Let x| and s^2 be sample estimates drawn randomly from a population with mean mu and variance sigma^2, and finite third central moment mu3. Find Cov(x|,s^2)
So, I set up the problem, trying to get the cov() into a form that I can do something with. I start with Cov()=E((x|-mu)(s^2-[(n-1)/n]sigma^2) and I write out the summation for x| and s^2, since they are calculated from n samples, and mess around with those(adding a subtracting mu and whatnot) and manipulate it, and for the expression (x|-mu)(s^2-[(n-1)/n]sigma^2), I get 1/n(x|-mu)*Sum[(xi-mu)^2]+n(x|-mu)^3-((n-1)/n)sigma^2 * (x|-mu) Does that look right? so what am I going to get when I take the expectation of this? how much simpler can I get it? it's not immediately apparent to me what sort of expression I'm supposed to manipulate cov() into, so I could be on the wrong track. Second question: I have a better feel for this, in that I have an Idea of what method I'm meant to be using. Find the pdf, and hence the expected value and variance, of the estimator x|. So, the method I'm meant to use, is use the moment generating function to find the distribution of Sum[xi], ad then the method of transformation to find x|=(1/n)*Sum[xi]. So that does sound too bad. While looking for the mgf, I want to be sure this step is valid; mgf(Sum[xi])= E(e^[t*Sum[xi]])=E(product(e^(t*xi)))=Product(E(e^(t*xi))) Where Product() denotes take the product over i. Is that last step valid? And what sort of transformation should I take? Anyway, thanks for any help you can give. -- -------------------------------------------------------------------------- Dennis O'Dea University of Illinois, Department of Economics www.students.uiuc.edu/~dodea [EMAIL PROTECTED] . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
