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The probability density functions (pdf's) of the fluctuating velocity components, as well as their first and second derivatives, are calculated using data from the direct numerical simulations (DNS) of fully developed turbulent channel flow. It is observed that, beyond the buffer region, the pdf of each of these quantities is independent of the distance from the channel wall. It is further observed that, beyond the buffer region, the pdf's for all the first derivatives collapse onto a single universal curve and those of the second derivatives also collapse onto another universal curve, irrespective of the distance from the wall. The kinetic-energy dissipation rate exhibits log normal behavior.