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If X and Y are independent variates and X+Y is a normal distribution, then both X and Y must have normal distributions. This was proved by Cramér in 1936.

The difference between a quantity and its estimated or measured quantity.

The ratio of two independent estimates of the variance of a normal distribution.

A grouping of statistics.

nu_((r))=sum_(x)x^((r))f(x), where x^((r))=x(x-1)...(x-r+1).

Any bivariate distribution function with marginal distribution functions F and G satisfies max{F(x)+G(y)-1,0}<=H(x,y)<=min{F(x),G(y)}.

gamma_r=(kappa_r)/(sigma^(r+2)), where kappa_r are cumulants and sigma is the standard deviation.

If a distribution has a single mode at mu_0, then P(|x-mu_0|>=lambdatau)<=4/(9lambda^2), where tau^2=sigma^2+(mu-mu_0)^2.

A set of statistical distributions having different variances.

A set of statistical distributions having the same variance.