Question

n 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

Goal: simulate independent at-bats where P(home run) = 0.10 and P(not) = 0.90.

Simple procedures (any one will do):

1) Using random integers 1–10
- For each at-bat generate a random integer uniformly from 1 to 10.
- If the number = 1, record "home run"; otherwise record "not a home run".
- Repeat for as many at-bats as you want.

2) Using a uniform random number on [0,1)
- For each at-bat generate U ~ Uniform(0,1).
- If U < 0.10, record "home run"; otherwise record "not a home run".

3) Using single random digits (0–9)
- For each at-bat pick one digit from 0–9 (e.g., from a random-digit table or generator).
- If the digit is 0 (or any one chosen digit), record "home run"; otherwise "not a home run".

Notes:
- Generate a new random value for each at-bat so outcomes are independent.
- To estimate long-run behavior, simulate many at-bats and compute the fraction of home runs; it should be close to 0.10.
- If using software, most libraries have a uniform random function you can threshold as in method 2.