<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

        Visit Stack Exchange

        Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

        -2
        votes
        0answers
        22 views

        Problem in understanding means of i.i.d. variable

        Let $X_i$ be i.i.d. and $X_i(\omega)= \omega, \omega \in (0,1)$, $P :=$ Lebesgue measure. Then I have $\bar X_n (\omega) = \frac{\sum^n_{i=1} X_i(\omega)}{n} = \frac{n \omega }{n} = \omega$. However,...
        0
        votes
        1answer
        46 views

        Expected sum of chosen coordinates in a random subset of a Hamming hypercube

        Let $S$ = $\{v_1, v_2, ..., v_n\}$ denote a random subset of a Hamming hypercube of dimension $d$, where $n = |S|$ and $n \leq 2^d$. If $v_i$ = $\langle x^i_1x^i_2... x^i_d\rangle$ for all $i \in [1,n]...
        4
        votes
        1answer
        112 views

        Nonlinear boolean functions

        Let $\mathbb{F}_2=\{0,1\}$ be the field with two elements. I wonder if there is any known algorithm/construction that, given any $n\geq 1$, returns a boolean function $f:\mathbb{F}^n_2\rightarrow \...
        -2
        votes
        0answers
        37 views

        What is the theoretical probability? [on hold]

        I have created a variation of the dice game PIG. In the game, you roll 1 die. If you roll a 1, your point total for that round is 0. If you roll a 2, your overall point total goes back to zero. ...
        1
        vote
        1answer
        59 views

        Generalization of inverse transform sampling

        If X is a random variable over an arbitrary alphabet, is there a (deterministic) function f() such that X = f(U), where U is a uniform random variable over the unit-interval?
        0
        votes
        0answers
        57 views

        Expected value of eigenvalue of matrix

        Let $A = (X_{ij})_{ij}$ a square matrix of size $n$ where the $X_{ij}$ are (discrete) real random non-negative entries. Denote by $\lambda_1(A) \geq \dots \geq \lambda_n(A)$ the (random) ordered ...
        5
        votes
        2answers
        151 views

        Probability of at least two of $n$ independent events occurring subject to some conditions

        Given a set of independent Bernoulli random variables $\{x_1, \dots, x_n\}$, let $p = \sum_{0<i\leq n}\Pr[x_i = 1]$ and $X=\sum_{0<i\leq n} x_i$. We know that for any $i$, we have $\Pr[x_i = 1]\...
        -2
        votes
        0answers
        31 views

        Sum of probabilities of events vs. probability of at least one event [on hold]

        $P_i$ is the probability of one event. As defined below, $a$ is the sum of all probabilities of events (that may or may not be independent), and $c$ is the overall probability that at least one event ...
        3
        votes
        0answers
        81 views

        Collecting proofs of the birth of the giant component

        I want to collect different proofs of Erd?s-Rényi result on the double jump of the largest connected component on $G(n,p)$ (or in $G(n,M)$. I know the original proof of Erd?s-Rényi, the proof that ...
        1
        vote
        1answer
        48 views

        gaussian isoperimetric result for minimal measure under translation

        Consider two spherical Gaussian distributions in $\mathbb{R}^n$, $A = \mathcal{N}(x, I)$ and $B=\mathcal{N}(y, I)$ where the difference in means is $\delta = y - x$. Let $S \subset \mathbb{R}^n$ be a ...
        3
        votes
        0answers
        157 views
        +50

        What happens in the martingale CLT if I norm by the conditional variance instead?

        TLDR: I'm a statistician (bear with me!) trying to use the martingale CLT but I only can estimate the conditional variance instead of the unconditional one. Can I do anything to get a CLT with norming ...
        -1
        votes
        0answers
        22 views

        Independence of stationary process and it's derivative

        Let $X(t)$ be a centred stationary gaussian process on the reals, with differentiable sample paths, with covariance function $r(t)$ Are $X(0)$ and $X'(0)$ independent? Why? Are they independent only ...
        -1
        votes
        0answers
        28 views

        Sigma algebra generated by two partitions [on hold]

        If $(A_1, ..., A_m)$ and $(B_1, ... B_n)$ are two partitions of $\Omega$, show that: (a) $(Ai\cap Bj)$ is a partition of $\Omega$. (b) $\sigma \{ \sigma\{A_i\} \cup \sigma\{B_j\} \} = \sigma \{ A_i ...
        1
        vote
        1answer
        41 views

        References for Hellinger distance/affinity involving mixture distributions

        For two continuous probability distributions $F,G$ and their densities, $f,g$, the (squared) Hellinger distance/affinity is given by $d^2_H(F,G)=1-\int_{\mathbb{R}} \sqrt{fg}~dx$. Suppose that $f,g$ ...
        2
        votes
        1answer
        73 views

        The effect of random projections on matrices

        Let $A\in\mathbb{R}^{n\times n}$ be a given normal matrix, i.e. $A^TA=AA^T$. Let $P_s\in\mathbb{R}^n$ be a random projection matrix to an $s$-dimensional subspace in $\mathbb{R}^n$. Suppose $\frac{A+...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>