I suspect X and Y here are random variables. pedantic interlude: ----- The word Gaussian applies to changes in both scale and location (standard deviation and mean) to the standard N(0,1) density d(x) = sqrt(1/2π) exp(1x^2/2), or in other words applying an affine linear function f(x) = ax + b to a standard Gaussian random variable X: Y = aX + b for any real numbers a ≠ 0 and b.) ----- So in fact an "orthogonal linear combination" of independent Gaussians like what Adam suggests will indeed result in a Gaussian. If the original ones are standard, then this careful linear combination will also be standard. (But it's also true that any affine linear combination of arbitrary Gaussian random variables, X_1 and X_2, like Y = a_1 X_1 + a_2 X_2 + b will result in Y's being Gaussian (unless it's degenerate). —Dan Adam Goucher écrit: ----- If I'm not mistaken, the Gaussian distribution is unique (up to scale) in that if X and Y are *independently* Gaussian, then every combination cos(theta) X + sin(theta) Y is also Gaussian. (Equivalently,, it's the only axisymmetric product distribution.) -----