The probability density function of the velocity fluctuations in turbulent pipe flow is directly obtained from the measured velocity-velocity correlation function by calculating the higher order spectral moments of the correlation function. The probability density function is assumed to be the product of a Gaussian and a Lorentzian. The Gaussian represents the distribution of the "active" velocity fluctuations : the velocity fluctuations which are typically rotational and actually participate in the turbulent cascade. The Lorentzian describes the velocity fluctuations that are inactive, i.e.,the "quiescent" velocity fluctuations which are nonparticipating in the turbulent cascade but are slightly excited by their turbulent environment. With increasing Reynolds number, the development of the turbulent flow towards a more space-filling state is clearly observed by an increase of the amount of active velocity fluctuations, Addition of a drag-reducing polymer to a turbulent flow is known to cause a large reduction of the turbulent energy loss. After we add such a polymer, a turbulent cascade is still observed, but it is confined to a very small fraction of the fluid volume. The polymer has caused a very large part of the flow to become "inactive" by a suppression of small velocity fluctuations in the bulk of the turbulent flow.