Recent content by jimholt

Cool, thanks a bunch. Just wanted to have another set of eyes look at it.

Really? No thoughts, suggestions, opinions?

If we have a partition \mathcal{P}=\{A_1,A_2\} of some set A, then we can talk about the sigma-algebra generated by this partition as \Sigma=\{\emptyset, A_1,A_2,A\}. How can I define this concept more generally? Here is what I have: A partition \mathcal{P} of some set A generates the...

Ok, so me thinks they are not in general independent. If we know G happened, we do indeed have information to update our probability of V (or W). E.g., if the probabilities over \Omega=\{HH,HT,TH,TT\} are given by the 4-vector (q,r,s,1-q-r-s), then \Pr(G \cap V) = \Pr(HH) = q , \Pr(G) =...

Homework Statement Let \Omega=\{HH,HT,TH,TT\} and let F and U be two partitions of \Omega: F=\{G,K\} with G=\{HH,TT\} and K= \Omega\backslash G, while U=\{V,W\} where V=\{HH,TH\} and W= \Omega\backslash V. If 2^\Omega is the \sigma-algebra of \Omega, and A=2^F and B=2^U...

Homework Statement I have the function f(p,q)=p(1-p)/[q(1-q)] where p and q are in (0,1). I want to say that if p is close to q, f(p,q) is 'close' to 1. What is a formal way of saying how close to p q should be? The Attempt at a Solution Basically I want to say f(p,q)= 1 + \epsilon(p,q)...

Yup, quite right. This brings up another confusing point for me, but let me chew on it a bit before starting a new thread. Thanks for lending me your eyes.

Not really a homework question, but here goes... Homework Statement If we have two (binary) random variables X and Y, and we know the probability mass function for X, as well as the correlation between X and Y, can we find the probability mass function for Y? Homework Equations Let f(x) be...

Doh. Made the same mistake twice, didn't I? I think I have it now. Cov(X,Y)=-1/4 and then \rho_{XY}=\frac{Cov(X,Y)}{\sigma_X\sigma_Y}=-1. Makes a lot more sense. Thanks for your help, LCKurtz!

Ah yes, thanks for that. I am rustier than I thought. Using the equation f(x,y) = f(x | y) \cdot f(y) then since f(x=0|y=1) = f(x=1|y=0) = 1 and f(x=0|y=0) = f(x=1|y=1) = 0, I do indeed get the correct joint pmf. But now, I am a little bit confused about the covariance between X and Y... We...

Obtain marginal probability mass function (pmf) given joint pmf Not really a homework question, but it does have a homeworky flavor, doesn't it... Homework Statement Given a join probability mass function of two variables, is it always possible to obtain the marginals? E.g., if I have a...