# Questions tagged [covariance]

Questions about covariance, a measure of (linear) association between two random variables.

471 questions
3k views

### Is a symmetric positive definite matrix always diagonally dominant?

A Hermitian diagonally dominant matrix $A$ with real non-negative diagonal entries is positive semidefinite. Is it possible to have a Hermitian matrix be positive semidefinite/definite and not be ...
177 views

328 views

126 views

55 views

### Is the positive part of a covariance stationary process also stationary?

I am wondering if it is possible to derive a result on the stationarity of the positive or negative part of a covariance stationary process. Namely, consider $\{ X_t \}, t=1,2,3,...,$ a covariance ...
661 views

107 views

294 views

70 views

### Simplify variance expression, taking into account covariances:$\operatorname{var}(Y_i-\bar Y-\hat {\beta}_1(x_i-\bar x))$

Find $\operatorname{var}(Y_i-\bar Y-\hat {\beta}_1(x_i-\bar x))$ where $\hat {\beta}_1=S_{xy}/S_{xx}$ is the least square estimator and $Y_i$ a random variable. I know that I can't simply split the ...
643 views

### Variance of a sum of identically distributed random variables that are not independent

I am "new" to probability/statistics and I was hoping someone could verify that this is correct. Let $Y_1,\ldots,Y_n$ be random variables that follow a common distribution with mean $\mu$ and variance ...
368 views

### Stationary Gaussian process whose correlation parameter approaches zero.

Consider a mean-zero ($\mu = 0$), unit-variance ($\sigma^2$) Gaussian random process $X(t)$. This process is strictly stationary (the joint-probability distribution does not vary with $t$). The ...
44 views

### What does it mean if $cov(f(x1), f(x2))$ is positive in the context of LHS sampling?

If cov(f(x1),f(x2)) is positive, does that mean f is close to symmetric along x1 and x2? I am struggling to put this into understandable terms. Edit: The context is equation 6 in this paper: http://...
84 views

### Means and Covariances of powers of a normal distribution

Let $X$ be a normally distributed random variable, with mean $\mu$ and variance $\sigma^2$. Consider a random vector $$V = \left[ X^n, X^{n-1}, \dots, X^2, X, 1 \right]^T$$ What is the expected ...
89 views

### Basic MVUE Application

I am having some trouble with the following problem: Let $X = (X_{1}, . . . , X_{n})$ a random sample from $f_{\theta}$, where $\theta \in \Theta$. Suppose that $W$ is the MVUE for $\theta$. Let $Z$ ...
468 views

### Expected value of the sample covariance

Let $X = (X_1,\dots,X_p)$ is a random (column) vector with values in $\mathbb R^p$. The covariance matrix $\mathrm{Cov}(X,X)$ is defined by $$\mathrm{Cov}(X) := E[(X-E[X])(X-E[X])^T]$$ By definition ...
For my study, as a part of a Matlab exercise, the following question is asked: Using the results of the estimated standard deviations of the random variable $x(k)$ for $k = 10^3; 10^4; 10^5$ ...
I'm practicing for an exam and a mock question has me completely stumped. If someone could show me the steps I would be very grateful! There are two random variables, $A$ and $B$. $Var(A) = 9$, and \$...