One‐dimensional and joint probability density distributions for longitudinal components of turbulent velocities as well as higher‐order correlations are measured in a turbulent boundary layer on a flat plate using hot‐wire anemometry and high‐speed computing methods. The effect of the nonlinear response of the hot‐wire is taken into account. Data pertaining to the general nature of the turbulent boundary layer are presented and comparison is made between the measured correlations and those corresponding to a Gaussian probability distribution of turbulent velocities as well as to non‐Gaussian distributions of the Gram‐Charlier type. Similar comparisons are made of the measured one‐dimensional and joint probability distributions. Probability distributions in the boundary layer are also compared to those measured downstream of a grid. The closure of the tails of the probability distribution and its effect on the accuracy of the measurements of higher‐order moments is considered.