Final answer:
DNA polymerase α is the eukaryotic enzyme with both a DNA polymerase and an RNA primase, which initiates the synthesis of Okazaki fragments by laying down an RNA primer followed by DNA extension.
Step-by-step explanation:
The eukaryotic DNA polymerase that has both DNA polymerase and RNA primase activity, which are responsible for initiating the synthesis of Okazaki fragments, is polymerase α. Its RNA primase subunit lays down a short RNA primer, and then the DNA polymerase subunit extends this primer with deoxyribonucleotides. In contrast, prokaryotic organisms like E. coli use a single RNA polymerase composed of five subunits (alpha, alpha, β, β', and σ) for transcription, with the σ subunit involved only in transcription initiation. Furthermore, in prokaryotes, the removal of RNA primer from Okazaki fragments is carried out by DNA polymerase I, different from the polymerase with primase activity in eukaryotes.