The joint probability density distributions,p(u,v), of theuandvturbulence components are presented for nine positions across a fully developed turbulent channel flow. These distributions were determined by using 512 000 pairs ofuandvvalues at each position and thus enable comparison of the relative character between the distributions. To show the contribution to the Reynolds stress, −&rgr;uv¯at each point in theu‐vplane, the distributions ofuvp(u,v) were determined. These distributions show the relative contributions touv¯as a function of position across the channel. Finally, the distributions ofp(u,v) are compared with those ofuvp(u,v). The most probable pairs of velocities do not produce the largest contribution touv¯.