Recent content by Cant or Wont

I'm not even halfway through my first Topology course so I wouldn't like to say what people usually assume! But I'm given to understand that when we talk about a Topology induced by a matric on X then the open sets U are those that if a \in U there is an r > 0 s.t. B \left( a,r \right)...

Seems to me the disagreement between you and your professor is that you have declared what you would like your topology \mathcal{T} to be instead of taking the topology that your metric d actually induces on \{1,2,4 \} ?

Sorry my bad you actually copied it correctly! It's been a long day! 2 is correct then. And yes that is the correct way to get the probability of A.

You know that \int_{1}^{2} f_{X} \left(x\right)dx=1 right? But \int_{1}^{2} 2x^{2}dx \neq 1 . So what you need is some c such that \int_{1}^{2}cx^{2}dx = 1. Can you see how to do that?

Someone posting the step by step will do little to help your understanding. How far have you got? Also this probably belongs in the Homework and Coursework forum and not here.

I like to think I'm capable of expressing myself using my hands in an infinite number of ways.

You could set it out as a binomial tree if you fancied? Reducing the outcomes to Black and Not Black - i know you said you wanted to do it without a tree diagram but binomial trees never get old. (Much like probability questions involving urns) This may, or may not, help you get a feel for...

Take the negative of the critical value in the table and reject if your t-value is less than this. I'm presuming you're doing a one-sided test on (<). In this instance you could take the absolute value and reject when t is greater than, but you can probably see how always taking the absolute...

Not sure just providing the correct answer will be enough here. When you say you "don't even understand what it's asking" how much do you know? If I were to ask you the expected value of a single dice roll would you know how to arrive at the answer to such a question?

A lot? Potentially none - X might be G measurable.

I don't know how the book you're following sets it out. But consider discrete random variables X,Z and the E(X|Z=z) for distinct z's and how the sigma algebra generated by Z partions Omega. So consider first the functions measurable wrt to the trivial sigma algebra. Then a richer sigma...

Are you trying to show that X + X ~ Po(2m) or that 2X ~ Po(2m)? And do you understand why these are not the same? (The earlier dice nicely shows you that they aren't so understand that) So if Z = X + Y, then P(Z=1) is the probability of the events {X=1} and {Y=0} or {X=0} and {Y=1}...