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The variance of a constant is zero. Var ( a ) = 0. {\displaystyle \operatorname {Var} (a)=0.} Conversely, if the variance of a random variable is 0, then it is almost surely a constant.
If the mean =, the first factor is 1, and the Fourier transform is, apart from a constant factor, a normal density on the frequency domain, with mean 0 and variance / . In particular, the standard normal distribution φ {\displaystyle \varphi } is an eigenfunction of the Fourier transform.
Uncorrelated random variables have a Pearson correlation coefficient, when it exists, of zero, except in the trivial case when either variable has zero variance (is a constant). In this case the correlation is undefined.
Z is a standard normal with expected value 0 and variance 1; V has a chi-squared distribution (χ 2-distribution) with degrees of freedom; Z and V are independent; A different distribution is defined as that of the random variable defined, for a given constant μ, by (+).
Random variables whose covariance is zero are called uncorrelated. [4]: 121 Similarly, the components of random vectors whose covariance matrix is zero in every entry outside the main diagonal are also called uncorrelated. If and are independent random variables, then their covariance is zero.
Throughout this article, boldfaced unsubscripted and are used to refer to random vectors, and Roman subscripted and are used to refer to scalar random variables.. If the entries in the column vector = (,, …,) are random variables, each with finite variance and expected value, then the covariance matrix is the matrix whose (,) entry is the covariance [1]: 177 ...
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) [1] states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. [2]