Hard Statistical Reliability Problem

**Hello everyone! I hope someone can help me with this problem :( been thinking about it but still couldn't come to a conclusion about how to do this part. #1 is the most important questions...**

1. Assume that 2 baseball reams have win records of .55 and .52. Demonstrate how to compute or estimate the number of games that must be played in order for the better team to win 50% of the time, 75% of the time, and 90% of the time. Validate your results by simulation.

**2. **Simulate a constant-rate process. Show that its mean and variance have the same limiting value.

**3. **Simulate a non-constant rate process. Show that its mean and variance are not necessarily the same.

**4. **Comment on your observations.