一个Algebra未必是 \sigma -algebra 例如\Omega=(-\infty, \infty], \mathcal{A} 定义为 \{\bigcup_{i=1}^n(a_i,b_i]:\infty \le a_i \le b_i \le \infty\} ,也就是所有左开右闭区间的可数并,那显然 \Omega\in \mathcal{A} ,并且 \mathcal{A} 对于有限并封闭,要证明它是一个代数...
任意A中元素的并集也在A中{1,2}显然不在 所以A这么选不是个sigma algebra 如果以上我理解的对，那么我依然有2个问题 1.声明一个概率测度空间的时候，这个sigma代数是所有符合条件的sigma代数的还是其中任意一个？2.这玩意除了写法高大上外和概率到底有啥本质的关系。。。请用人话给一个可视化的例子被 首先你...
测度与概率 sigma-field/sigma-algebra 30:30 测度与概率 measure 01:21:41 测度与概率 measure extension---motivation 39:50 测度与概率 measure extension---outer measure 28:39 测度与概率 measure extension---construction of an outer measure 39:39 测度与概率 measure extension---a sigma field...
1-5 sigma-代数 sigma-algebra/field是【自学用】高等概率论: 概率空间与随机变量的第7集视频,该合集共计28集,视频收藏或关注UP主,及时了解更多相关视频内容。
半代数(Semi-algebra)是连续区间内所有左开右闭区间的集合，直观且构造简单。半代数需满足三条性质以成为半代数。进一步，Algebra定义集合对有限并、有限交和补封闭，而\(\sigma\)-Algebra则要求对可数并、可数交和补封闭。\(\sigma\)-Algebra的生成与验证 \(\sigma\)-Algebra的生成通过从特定集合开始...
be a sub-sigma-algebra of (i.e., is a sigma-algebra and ). Let be an event. We say that a random variable is a conditional probability of with respect to the sigma-algebra if and only if It can be shown that this definition is equivalent to our definition of probability conditional...
In mathematical analysis and in probability theory, a σ-algebra on a set X: is a collection \Sigma of subsets of X including X itself, it is closed under complement,
Sigma-algebrameasureprobability spacerandom variabledistributionBorel setscumulative distribution functionIn reviewing the foundations of probability, to establish the underpinnings of the Monte Carlo method, I found some basic results for which I could not find a simple, clear, and concise derivation in ...
The presentation is pitched at the level of Monte Carlo practitioners, rather than mathematical probabilists. 关键词: Sigma-algebra measure probability space random variable distribution Borel sets cumulative distribution function DOI: 10.1515/MCMA.2008.009 被引量: 6 年份: 2008 ...
Let $(X,{\\mathcal A},\\mu )$ be a probability space, where ${\\mathcal A}$ is the Borel $\\sigma $-algebra with respect to a given metric $d$ on $X$. We s... ND Markoulakis,ΝικλαοΔΜαρκουλκη 被引量: 3发表: 0年 ...