Given a random variable $\beta \in R$ with zero mean and variance $\sigma^{2}$. What is the mean of the random variable $z=\beta^{2}$?
The answer is $\sigma^{2}$. Why is it not $\sigma^{4}$?
2026-04-01 03:10:05.1775013005
Given a random variable $\beta \in R$ with zero mean and variance $\sigma^{2}$. What is the mean of the random variable $z=\beta^{2}$?
64 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 STATISTICS
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Statistics based on empirical distribution
- Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$
- Fisher information of sufficient statistic
- Solving Equation with Euler's Number
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- Determine the marginal distributions of $(T_1, T_2)$
- KL divergence between two multivariate Bernoulli distribution
- Given random variables $(T_1,T_2)$. Show that $T_1$ and $T_2$ are independent and exponentially distributed if..
- Probability of tossing marbles,covariance
Related Questions in RANDOM-VARIABLES
- Prove that central limit theorem Is applicable to a new sequence
- Random variables in integrals, how to analyze?
- Convergence in distribution of a discretized random variable and generated sigma-algebras
- Determine the repartition of $Y$
- What is the name of concepts that are used to compare two values?
- Convergence of sequences of RV
- $\lim_{n \rightarrow \infty} P(S_n \leq \frac{3n}{2}+\sqrt3n)$
- PDF of the sum of two random variables integrates to >1
- Another definition for the support of a random variable
- Uniform distribution on the [0,2]
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
Related Questions in VARIANCE
- Proof that $\mathrm{Var}\bigg(\frac{1}{n} \sum_{i=1}^nY_i\bigg) = \frac{1}{n}\mathrm{Var}(Y_1)$
- $\{ X_{i} \}_{i=1}^{n} \thicksim iid N(\theta, 1)$. What is distribution of $X_{2} - X_{1}$?
- Reason generalized linear model
- Variance of $\mathrm{Proj}_{\mathcal{R}(A^T)}(z)$ for $z \sim \mathcal{N}(0, I_m)$.
- Variance of a set of quaternions?
- Is the usage of unbiased estimator appropriate?
- Stochastic proof variance
- Bit of help gaining intuition about conditional expectation and variance
- Variance of $T_n = \min_i \{ X_i \} + \max_i \{ X_i \}$
- Compute the variance of $S = \sum\limits_{i = 1}^N X_i$, what did I do wrong?
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?
We have that $$ \operatorname E\beta^2=\operatorname E(\beta-0)^2=\operatorname E(\beta-\operatorname E\beta)^2=\operatorname{Var}\beta=\sigma^2. $$ The expected value of $\beta^2$ is equal to the variance of $\beta$ since the mean of $\beta$ is equal to $0$.