Hello, everyone, I want to resolve one optimal problem, with the following probability inequality constraint. $Pr(h^H(W_1 - W_2 -W_3 -U)h \geq \sigma^2) \leq \rho$ where $h \sim …

Consider an experiment consisting of a repeated trial with two random Bernoulli (=binary) variables, A and B. Each trial consists of multiple outcomes for both A and B. Each trial …

Suppose sensor nodes of homogeneous sensing ranges are dropped by Poisson distribution around the given rectangle of area l*h. How do i calculate the minimum number of circles requ …

suppose sensors of homogeneous radius r are dropped by Poisson distribution on a straight line of length L. how to calculate that the straight line is covered by sensors with prob …

for example, x is random variable, f(x) and g(x) are two "very very" different distribution functions. It is impossible to calculate variance analytically, so if we want to compare …

recently, i need to compute this kind of integral: $$ \int ^\infty _c \Phi(ax+b) \phi(x) dx$$ where a, b and c are all constants and $\Phi(x)$ denotes the CDF of standard normal di …

Hi, I have a random variable V with probability density g(V) and a sigmoid, or logistic, function Y=S(V). I'd like to calculate a closed-form expression for the expected value of t …

Prove the (numerically-evident) proposition that \begin{equation} \Sigma_{i=0}^\infty f(i) = 1, \end{equation} where \begin{equation} f(i)= 2^{-4 i-6} q(i) \frac{\Gamma(3 i+\frac{ …

One of my friends is building a game where the player will get questions from 6 different categories. Each category has a total of 50 questions. A single game consists of answering …

I'm trying to proving the stable limit of a martingale M_n(t). When I calculate the limit in probability of its quadratic variation, I find that it is always null except for a poin …

x is a normal distributed variable. then what is the expectation of ln(1+e^x). i simulated this distribution and find that when x is N(0, 100), the mean of this function is around …

Suppose there is an oracle that returns a number $b \in \mathbb{Z}_{n}$ whenever I press the button. We have $b = a + e$, where $a \in \mathbb{Z}_n$ is a fixed number and $e$ is s …

Let me explain what I mean: The width of the average person varies, perhaps with a normal distribution. Given a specific variance, how many people (on average) can sit side-by-si …

I asked this question on http://math.stackexchange.com/questions/377140/random-variables-related-through-nonlinear-system-of-equations, however I received no answer for a while so …

In the context of the Bingham probability distribution the ${ }_1F_1$ hypergeometric function of matrix argument naturally arises as a normalization constant of the probability dis …