郭富城徐静蕾情爱视频

Questions tagged [probability-theory]

Use this tag only if your question is about the modern theoretical footing for probability, for example probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for specific problems and explicit computations. Use [tag:probability-distributions] for specific distribution functions, and consider [tag:stochastic-processes] when appropriate.

过滤
排序
标记为
0
票数
0答案
6浏览

带有替代假设的Martingal收敛定理

有谁提供包含以下定理证明的资料(书籍,论文等)? Let $(X_n)_{n\in\mathbb{N}_0}$ a sequence of nonnegative random variables adapted to a filtration $(\mathcal{F}_n)...
2
票数
0答案
24浏览

If $\mathbb{P}(A_n)\to 0$, prove that $\int\limits_{A_n}X\mathrm{d}\mathbb{P}\to 0.$

Let $(\varOmega,\mathcal{F},\mathbb{P})$ be a probability space. If $X:\varOmega\to \mathbb{R}$ is integrable and $(A_n) \subset\mathcal{F}$ such that $\mathbb{P}(A_n)\to 0$, then prove that $\int\...
1
投票
0答案
12浏览

博纳'L定理é维's theorem

Bochner's Theorem: If $\varphi : \mathbb{R}^d \to \mathbb{C}$ is positive definite, continuos and $\varphi(0)=1$ then it is the characteristic function of a probability measure, i.e. the Bochner's ...
1
投票
0答案
26浏览

证明如果级数收敛,那么大数定律成立。

Let $(X_n)_{n \geq 1}$ be a sequence of pairwise independent random variables such that : $$\sum_{n=1}^{\infty} n^{-1} P\left\{\max _{1 \leq m \leq n}\left|\sum_{k=1}^{m}\left(X_{k}-E X_{k}\right)\...
2
票数
1回答
34浏览

将CLT应用于由两个iid随机变量序列组成的随机变量

第2年统计数据 Q: Suppose you have a sequence $X_1, X_2, ...$ of iid random variables with mean $E(X_1)=\mu_X$ and variance $Var(X_1)=\sigma^2_X$ and another sequence $Y_1, Y_2, ...$ of iid random ...
0
票数
0答案
13浏览

非负扩展实函数一致收敛时的交换极限和有限加性积分

Let $(X, \mathcal X)$ be a measurable space, and let $\mu$ be a finitely additive probability measure on $(X, \mathcal X)$. If $f$ is an extended-real-valued simple $\mathcal X$-measurable function of ...
0
票数
1回答
26浏览

为什么特征函数应该是正定的?

Suppose $X$ is a $\mathbb{R}^d$-valued random variable. Suppose $(t_k)_{1 \leq k \leq n} \subset \mathbb{R}^d$ and $(z_k)_{1 \leq k \leq n} \subset \mathbb{C}$. Why should hold that if $\phi$ is the ...
0
票数
1回答
42浏览

为什么使用随机变量代替概率空间

在讨论各种概率模型时,许多作者更喜欢使用随机变量,而不是概率分布。当然,这种不同点更重要...
0
票数
0答案
12浏览

小于零的随机变量和Hoeffding的线性组合'不等式

设$ X_1 $和$ X_2 $为均匀随机变量并设置 $$X = aX_1 + bX_2, $$ with $a \geq 0$ and $b \leq 0$. I'd like to bound $P(X \leq 0)$ using Hoeffding's inequality. How do I do that? 附注:我...
0
票数
0答案
12浏览

帕累托定律和专业化的产物

让: $\lambda >0, ~~ \theta >1$ $f_X(t)= \frac{\lambda}{\theta} \big( \frac{\theta}{ t} \big) ^{ \lambda +1 } \mathbb{1}_{t > \theta}$ $(X_i)_{i \geq 1}$ are independent and follow the ...
0
票数
1回答
26浏览

Show that the median minimizes $E[|X-c|]$.

The following proof follows from the answer of @grand_chat. I slightly change the proof, and it gives the different result, and I am wondering why it does not work. 令$ m $为$ X $的中位数。 ...
1
投票
1回答
54浏览

悖论?大数定律vs期权理论

掷一个公平的硬币:如果获得正面,您将赢得120,如果获得正面,您将获得0。 您会花多少钱玩这个游戏? 60对吗? 现在让我们考虑以下情况: 您的资产S ...
0
票数
0答案
28浏览

斯鲁茨基'中心极限定理的s定理

Assume $\sqrt{n}(X_n-X)\overset{d}{\to} N(0,\sigma^2)$ and $Y_n\overset{p}{\to} c$, where $X$ is a random variable and $c$ is a positive constant. Does it hold that $\sqrt{n}(Y_nX_n-cX)\overset{d}{\to}...
0
票数
1回答
35浏览

平斯克'度量空间的不等式!

假设$ p $和$ q $是可数集合$ X $的两个概率分布。然后定义$ p $和$ q $之间的总变化距离$ V(p,q)$如下: \begin{equation} V(p,q)=\frac{1}{2}\sum_{...
0
票数
0答案
22浏览

这是有限加性概率论的一种有趣的收敛方式吗?

这是一个软问题。我有兴趣听取社区提供的任何意见或反馈,并且不希望找到具体问题的解决方案。 以标准尺寸...

15 30 50 每页