This thesis presents the results from the investigation of time dependent B{sub d}{sup 0} {bar B}{sub d}{sup 0} mixing in B {yields} lepton X, B{sub d}{sup 0} {yields} D*{sup -} {yields} {bar D}{sup 0} {pi}{sup -}, {bar D}{sup 0} {yields} K{sup +} {pi}{sup -} channel in p{bar p} collisions at {radical}s = 1.8 TeV using 110 pb{sup -1} data collected with the CDF detector at the Fermilab Tevatron Collider. The {bar D}{sup 0} vertex is reconstructed. The B{sub d}{sup 0} decay length is estimated using the distance from the primary vertex to the measured position of the D{sup 0} vertex. The B{sup 0} momentum is estimated using the D{sup 0} momentum and a kinematic correction factor from Monte Carlo. With the dilution floating, {Delta}M{sub d} = 0.55 {+-}{sub 0.16}{sup 0.15} (stat) {+-} 0.06 (syst)ps{sup -1} is measured.