A mathematical study utilizing the statistics of noise theory is presented which derives light spot brightness probabilities for PPI target returns of various signal‐to‐noise ratios. An idealized model is employed which differs from similar previous ones by taking account of the cathode‐ray tube's highlight brightnessvsintensifier electrode voltage characteristic. For the 10KP7 cathode‐ray tube this characteristic obeys an approximate 2.5 power law in typical operation. This law, together with a square law second detector, combine to form an over‐all fifth power detector. The light spot brightness of the display is assumed to be formed by linear superposition of individual target returns resulting from the radar antenna scan. In the model, seven identical returns are so integrated.Various mathematical methods of handling the problem are considered. The Edgeworth series approximation is found to give poor results compared with the Laguerre polynomial approximation. By the latter method the light brightness probabilities are found to be obtainable by interpolation from a table of the incomplete gamma function. Ancillary tables of statistical moments and selected values of the confluent hypergeometric function,1F1(−5n/2; 1; −x), are included in the text.