Recent content by azdang

Yep, that's definitely what the problem says so, I'm not sure. What you've shown definitely seems right and I'm assuming it works for other cases when k is something else, as well. I'll check it out and ask my teacher about it if need be. Thanks!

Well, we are looking for the limit of a^2. Does that make a difference? Also, you said you got the same thing as me, but I'm a little confused how what you wrote (even though I know it's for the specific k=3 case) is the same as what I got. I'll look at it again to see if I can see the...

Let X be a Binomial B(\frac{1}{2},n), where n=2m. Let a(m,k) = \frac{4^m}{(\stackrel{2m}{m})}P(X = m + k). Show that lim_{m->\infty}(a(m,k))^2 = e^{-k^2}. So far, I've found that P(X = m+k) = (\stackrel{2m}{m+k}) \frac{1}{4^m} Then, a(m,k)=\frac{m!m!}{(m+k)!(m-k)!}. But I have no...

Ohh okay! So, wouldn't f^{-1}(E)= \Omega? And E is in E, so I think this works.

Let f be a function mapping \Omega to another space E with a sigma-algebra[/tex] E. Let A = {A C \Omega: there exists B \epsilon E with A = f^{-1}(B)}. Show that A is a sigma-algebra on \Omega. Okay, so I should start by showing that \Omega is in A. I wasn't sure if this was as easy as saying...

Let f be a function mapping \Omega to another space E with a sigma-algebra[/tex] E. Let A = {A C \Omega: there exists B \epsilon E with A = f^{-1}(B)}. Show that A is a sigma-algebra on \Omega. Okay, so I should start by showing that \Omega is in A. I wasn't sure if this was as easy as saying...

Oops, forgot to tackle part of the question: If F is still a sigma-algebra if B is a subset of Omega that does not belong to A. My thoughts are that it is still a sigma-algebra because I didn't seem to use the fact that B is in A at all in the proof that F is a sigma-algebra. Would that be correct?

Oh cool! Thank you again. You've been really helpful on these sigma-algebra problems. They are something I have never seen in all my years of math, so it's kinda tricky to get used to. Have a good day!

Yeah, that was the part I was iffy about. Let's see. So, B-(a\cap B) would be all the things in B not also in A. Could we say this is the same as B-a? If so, isn't that just B \cap a^c, which would be in F since a^c is an element of A.

Yeah, I know. We can blame my book for that, although it is 'script' A for the sigma-algebra, which I tried to show by making it Bold and Italicized. Well, the first requirement is that B would have to be in F. B could be represented as O intersect B, since O would be an element in A. The...

Okay, so basically, the B is fixed, but the A could represent any of the elements in sigma-algebra A. So for F, we could have: A n B Ac n B = (A U Bc)c B n B = B Bc n B = {} (A U B) n B = B O n B = B {} n B = <-- A little confused, is this {} or B I think I'm beginning to see why F...

I have another sigma algebra question. This one may be primarily in part to the fact that I just don't understand what the question is saying. It says: Let A be a sigma-algebra of subsets of \Omega and let B be an element of A. Show that F = {A \cap B: A is in A} is a sigma-algebra of subsets...

Ooh, thank you so much, Dick! I have a bunch of these to work on, so I could be back for some clarification. Thanks again! :)

Is it something like U[a + \frac{1}{n}, \infty) from n=1 to infinity, and that would be equal to (a, \infty)?

I am working on the last step of a proof to show that \sigma(O) = \sigma(C2). C2 = {(-\infty, a): a \epsilon R and O = all the open sets in R1. I have already showed that \sigma(C2) C \sigma(O). I am now trying to show the converse, that \sigma(O) C \sigma(C2). To do this, I know I just...