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Jul
30
comment what is difference between probability and probability space?
@JackBauer By the by, reading your answer (which, frankly, I had not done before), I find dangerous approximations in it. To begin with, what is the set $\Omega$ you are suggesting in the case at hand? "Tossing a coin until the first head is observed" requires an infinite sample space, there are none in your post, unless one counts as one the set homeomorphic to $\mathbb N$ which you explain before considering the sigma-algebra. Later on, I do not understand $H\subset\mathfrak F$. For which $(\Omega,\mathfrak F)$? Which event $H$? But then $H\in\mathfrak F$, not $H\subset\mathfrak F$? Ad lib.
Jul
30
comment what is difference between probability and probability space?
.../... send back the OP to a course for a full context of their question, then, rather surprisingly (to me), you more or less provide some snapshots of the contents of such a course. This is your choice, but there are others, at least as coherent.
Jul
30
comment what is difference between probability and probability space?
@JackBauer You are entitled to your opinion but the question asks "Are probability and probability space (are) different?" and for an example. My answer provides exactly that. Is asking questions on the site preferable to following a structured decent course in probability theory? No. Is it our task to answer this question by providing a course in probability theory? IMHO, no, our task is to answer this question as it is formulated (which my answer does). In this regard, if I may, I think that your answer balances between two points of view: first, you basically (and rightfully) .../...
Jul
30
comment Question about two sequences with a common limit
?? Alternatively $1$ and $3\cdot2^{2n}-1$.
Jul
30
comment Evaluating $\lim_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$
The crucial step is the existence of a dominating function, necessary to the convergence at the end, which, unfortunately, is not proved.
Jul
30
comment How to find PDF of ordered random variables?
Still at zero personal input (as you are probably well aware).
Jul
30
reviewed Approve What is the actual geometric meaning of trigonometric operations such as adding cos,sine,tan
Jul
30
reviewed Leave Closed How to count the real roots of a quartic equation?
Jul
30
reviewed Close E as an expectation of a quadratic form
Jul
30
reviewed Close Verify the following assertion:
Jul
30
reviewed Close Proving that a sequence converges or diverges
Jul
30
reviewed Close How to denote an even number in mathematics?
Jul
30
reviewed Close This expression is always a perfect square
Jul
30
reviewed Close Interest Question
Jul
30
reviewed Close Estimate what percentage of math articles on Arxiv are eventually published.
Jul
30
reviewed Close The Dual of a Dual problem for Convex Optimization Problem
Jul
30
reviewed Close System of equation problem
Jul
30
reviewed Close The Probability one Player will have more Kills than another based on a distribution of Kills?
Jul
30
reviewed Close how to prove the adjoint operator of the bounded linear operator is the bounded linear operator
Jul
30
reviewed Close Questions about Variance and Covariance