I'm not sure
- whether this is always true? and
- If it is true, whether it is a trivial assertion to make?
I've tried integrating using the definition of expectation, but I'm not getting anywhere with it.
2026-04-01 11:11:59.1775041919
Is it true that $\mathbb{E}|X-\mathbb{E}(X)|=0$ where $\mathbb{E}(X) $ is finite?
44 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PROBABILITY
- How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?
- Is this a commonly known paradox?
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- Prove or disprove the following inequality
- Another application of the Central Limit Theorem
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- A random point $(a,b)$ is uniformly distributed in a unit square $K=[(u,v):0<u<1,0<v<1]$
- proving Kochen-Stone lemma...
- Solution Check. (Probability)
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
Related Questions in EXPECTED-VALUE
- Show that $\operatorname{Cov}(X,X^2)=0$ if X is a continuous random variable with symmetric distribution around the origin
- prove that $E(Y) = 0$ if $X$ is a random variable and $Y = x- E(x)$
- Limit of the expectation in Galton-Watson-process using a Martingale
- Determine if an Estimator is Biased (Unusual Expectation Expression)
- Why are negative constants removed from variance?
- How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?
- $X_1,X_2,X_3 \sim^{\text{i.i.d}} R(0,1)$. Find $E(\frac{X_1+X_2}{X_1+X_2+X_3})$
- How to calculate the conditional mean of $E(X\mid X<Y)$?
- Let X be a geometric random variable, show that $E[X(X-1)...(X-r+1)] = \frac{r!(1-p)^r}{p^r}$
- Taylor expansion of expectation in financial modelling problem
Related Questions in MEANS
- Arithmetic and harmonic mean of two numbers.
- Mean and variance of $X:=(k-3)^2$ for $k\in\{1,\ldots,6\}$.
- Reason generalized linear model
- How do you calculate the probability of the difference between two normal distribution
- Calculating standard deviation without a data set.
- Compute the variance of $S = \sum\limits_{i = 1}^N X_i$, what did I do wrong?
- Find out if $\hat{\tau}$ is an unbiased estimator
- Computing mean and variance of custom distribution
- Prove $\lim\limits_{n \to \infty} \frac{\log (n!)}{n \sqrt[n]{\log 2 \cdot \log 3 \cdots \log n}}=1$
- How to tell when a data series is a normal distribution
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It is true if and only if $X$ is a constant random variable. Reason: $|X-\mathbb E X|$ is non-negative random variable and its expectation can be $0$ only when it is zero almost surely.