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How to linearize nonlinear stochastic differential equation [closed]

I need to linearize this stochastic differential equation:$dX(t)=X(t)(1-X^{2}(t))dt+X(t)dBt$so i can calculate $EX(t), EX^{2}(t), EX^{3}(t)$Pleas help me :)

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Upper bound for the expectation of a random variable times an indicator function

Suppose we have a random variable $X$. Is there any way of deriving an upper bound of the following expectation:$$E[X * \mathbf{1}_{X\ge x_0}],$$where $\mathbf{1}_{()}$ is an 0-1 indicator function,...

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Does the inequality $E[X^3] \geq E[X]E[X^2]$ hold for non-negative random...

My intuition says no, but I couldn't propose a clean counterexample:for example, for any binary r.v. $P[X = a] = p, P[X = b] = 1 - p$ where $a, b > 0$, I found that$$E[X^3] - E[X]E[X^2] = p(1 - p)(a...

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Expected value of two dependent Bernoulli random variables.

I'm in the process of finding $E(XY)$ where X and Y are non-independent Bernoulli random variables with both of them with probability of $\frac{n}{N}$I understand that $E(XY)=\Sigma\Sigma...

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Does $|x| \leq |y|$ imply $|\mathsf E[x]| \leq |\mathsf E[y]|$?

Does $|x| \leq |y|$ imply $|\mathsf{E}[x]| \leq |\mathsf{E}[y]|$?

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Does $|\mathsf{E}(xy)|\leq |\mathsf{E}(x)| \cdot |\mathsf{E}(y)|$ hold?

Does $|\mathsf{E}(xy)|\leq |\mathsf{E}(x)| \cdot |\mathsf{E}(y)|$ hold for any random variable $x$, $y$? Here $\mathsf{E}$ is the expectation.

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Cutting a stick randomly into 3 pieces - What is the expected length of the...

Problem Statement: Given a stick of length 1, the stick is to be cut randomly into 3 pieces. What is the expected length of the shortest stick?Attempt:Let $S$ be the random variable for the shortest...

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Independence of Bernoulli random variables defined by a uniform random number

Suppose we choose a random number $b$ from the interval $[0,1]$ with a uniform distribution. Based on this number, we define the following random variables:$$X_n=\begin{cases}1 & b\in...

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Is there a way to calculate $E\left[\mathrm{sgn}(X)X^n\right]$ if I don't...

I need to calculate $E\left[\mathrm{sgn}(X)X^n\right]$, where $\mathrm{sgn}(X)$ denotes the sign of the random variable $X$. I don't know the pdf for $X$, so I can't do the calculation directly. I know...

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Find the expected value of $\max\limits_{1\leq i\leq n} x_i -...

Choose $n$ numbers $x_1,\cdots, x_n$ uniformly and independently from $[0,1]$. Find the expected value of $$\max_{1\leq i\leq n} x_i - \min_{1\leq i\leq n} x_i$$The numbers $x_1,\cdots, x_n$ form a...

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Computing the expectation of the minimum difference between $0$-th i.i.d....

Let $X_0,X_1,\dots,X_n$ be independent random variables, each distributed uniformly on [0,1].Find $$ E\left[ \min_{1\leq i\leq n}\vert X_0 -X_i\vert \right] $$.Would any member of this...

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Expectation of function of dependent random variables

Consider a real valued function $h$ on random variables, and the following sample-average function $h_S(X_1, X_2, ..., X_n) = \frac{1}{n}\sum_{i=1}^n h(X_i).$ Assume $X_1, X_2, ..., X_n$ are not...

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Determining Perfect vs. Imperfect Information in Calculating Expected Value

In this scenario, you are presented with an opportunity to engage in a game for a fee of $50. On a table, there are two boxes: a large box and a small box. The large box contains a total of 40 balls,...

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Parsing an expectation problem about daily stock prices

Daily price movements of an asset are independent, and it is twice as likely for the price to go up than down. Let D represent the difference between the up and down movements of an asset that is sold...

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What is the expected value of the expected distance of a leaf from the root...

Let $T$ be a full binary tree that is randomly chosen with the same probability from the set of all the full binary trees with $n$ leafs. What is the expected value of the expected distance of a leaf...

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Expected value and variance of the random binary number generator

Problem from an old exam:The random number generator $X$ produces random numbers following a Poisson distribution with parameter $\lambda$. Unfortunately, these numbers are too small, so we decided to...

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Finding expectation of coordinates in random walk

This is Example 2(i) of Sheldon Ross' A First Course in Probability.I have a question about a variation of this problem:Consider a particle initially located at a given point in the plane, and suppose...

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A disc contains $n$ random points. Each point is connected to its nearest...

A disc contains $n$ independent uniformly random points. Each point is connected by a line segment to its nearest neighbor, forming clusters of connected points.For example, here are $20$ random points...

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Expected value of the number of vertices more than 2 edges apart in a random...

We create a random graph with $n$ vertices in such a way that for each pair of vertices $\{i, j\}$, we connect them with an edge with probability $p$ (each time drawing independently). Let $X$ be the...

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Satistics Dice Example [closed]

2 dices are thrown and values are categorized into 3 color groups (2-6) is of red group , 7 for blue and (8-12) is of green. And if there's a series of thrown values are also given fine the probability...

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