The statistics of a polymer chain has been conventionally investigated mainly by scattering. Instead, we theoretically examine the possibility of obtaining the statistics from single molecular observation. Motivated by this we discuss the statistical distribution of an ideal linear chain with its ends constrained, which could be directly obtained in principle by an experiment on an optically tweezed single molecule. We also derive the scattering function pertinent to the situation. Our consideration could open a way to experimentally study the statistics of a linear polymer chain with the ends fixed to obtain that of a ring polymer in lower dimension. (C) 2007 Elsevier B.V. All rights reserved.