Recent content by tjm7582

dacruick essentially gave you the "equation" that you would need to figure out what program they used. All random number generators create a deterministic sequence. Once you know what RNG was used and the seed that was used to start the sequence, you would have exact knowledge of the rest of the...

In the above example, if we take w to be a member of S, isn't it the case that S is the following Cartesian product: S={1,2,3,4,5,6}*{1,2,3,4,5,6}? Thus, if X1(w) is a random variable that is the "first roll of the die," X1() is nothing more than the coordinate projection defined on S, correct?

I guess I am still a bit confused. Consider, for example, the case of a stochastic process that is just two indexed random variables, X1 and X2. Each random variable is defined on the same domain, O. A realization of the stochastic process consists of a "draw" from O for each of the random...

I have been trying to learn some measure-theoretic probability in my spare time, and I seem to have become a bit confused when it comes to defining a probability measure on a sequence of random variables (e.g., the Law of Large Numbers). Most texts start by defining a random variable X{i}...

tim_lou, Thanks for the help. Are you referring to "baby" Rudin (Principles of Mathematical Analysis), or his other analysis book? I am away from my books, but I look forward to going over this when I return. Tom

Thanks for the replies. There has been no mention of a matrix topology, and a norm has never been defined when this claim of continuity was made. This is actually why I was so confused and felt that I was missing something entirely (that is, was the result was so obvious that it needed no...

When doing some self-study in probability, I have seen a number of authors state, without proof or justification, that the inverse of a matrix is continuous. For instance, a passage in a popular econometrics text (White (2001)) reads: "The matrix inverse function is continuous at every point...