  We consider two versions of discrete time totally asymmetric simple exclusion
processes (TASEPs) with geometric and Bernoulli random hopping probabilities.
For the process mixed with these and continuous time dynamics, we obtain a
single Fredholm determinant representation for the joint distribution function
of particle positions with arbitrary initial data. This formula is a
generalization of the recent result by Mateski, Quastel and Remenik and allows
us to take the KPZ scaling limit. For both the discrete time geometric and
Bernoulli TASEPs, we show that the distribution function converges to the one
describing the KPZ fixed point.
