Step 1: Understanding the Concept
In the RNA world view, RNA was the first genetic material and also acted as a catalyst.
Step 2: Statement I
Some RNAs such as the peptidyl transferase of the ribosome and self-splicing introns speed up reactions.
Catalytic RNA is called a ribozyme, so the statement is correct.
Step 3: Statement II
Repeated replication and mutation of early RNA produced many RNA molecules of different sequences and sizes.
So this statement is also correct.
Final Answer:
Both statements are correct.
\[ \boxed{\text{(A) }\text{Both statement I and statement II are correct.}} \]