Norm of random vector plus constant Suppose that $w$ is a multivariate standard normal vector and $c$ a real vector of the same size. I know that for positive x
$$P(||w+c||^2\geq x)\  \geq \ P(||w||^2\geq x)$$
but I cannot prove it. We use the euclidean norm , in dimension 2 or 3 drawings show that the inequality above holds, but I need a proof. 

We can prove it using Prékopa–Leindler inequality, see en.wikipedia.org/wiki/Pr%C3%A9kopa%E2%80%93Leindler_inequality
