The third and fourth intensity moments are calculated for a stochastic electromagnetic field whose quadrature components obey joint Gaussian statistics. From these moments the skewness and excess coefficients are derived and compared to the expressions for Rice-Nakagami and log normal statistics. The joint Gaussian intensity moments depend on three moments of the scattered electromagnetic waves, the inphase and quadratrue variances and the correlation coefficient; these three moments are calculated in the first Born approximation to illustrate application of the joint Gaussian results to interplanetary radio star scintillations. With this approximation, observations of skewness versus scintillation index are related to combinations of correlation length and spectral index for the solar wind electron number density fluctuations. This weak scattering relationship suggests a number of observational tests of the joint Gaussian hypothesis.