We derive a closed form expression for the marginal probability density function (pdf) for the weight vector coefficients in a minimum variance distortionless response (MVDR) adaptive beamformer, when the snapshots are i.i.d. normal, and the weights are computed via sample matrix inversion. The marginal pdf allows one to determine the dynamic range required to avoid saturation (with a specified degree of probability) in digital and/or analog implementation of beamforming weights.