Question

In analyzing a baseball team’s performance over several seasons, the coach ​observed that a particular baseball player hit a home run once every 10
​times at bat.
​
​Part A
Explain a procedure for using a random number generator to ​simulate the baseball player’s hitting outcome as either a homerun or ​not a homerun assuming the pattern continues as described above.

Answer 1

You want a simulation that makes each at-bat a home run (HR) with probability 1/10 and not a home run with probability 9/10. Here are two simple procedures depending on what your random number generator produces:

1) If your generator gives a uniform integer 1–10 (or 0–9)
- Generate a random integer from 1 to 10.
- If the number is 1, record a home run; otherwise record not a home run.
- Repeat for each at-bat.

(If the generator returns 0–9, treat one chosen digit—say 0—as “HR” and the others as “not HR”.)

2) If your generator gives a uniform real number between 0 and 1
- Generate a random number r in [0,1).
- If r < 0.10, record a home run; otherwise record not a home run.
- Repeat for each at-bat.

Notes:
- Repeat the chosen step for every at-bat to simulate a season or many seasons, then tally HRs.
- The trials should be independent (use a fresh random draw each time).