Question

(a)
In analyzing a baseball team’s performance over several seasons, the coach ​observed that a particular baseball player hit a home run once every
​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

Let the player hit a home run once every k at-bats (so the probability of a home run on any one at-bat is p = 1/k).

Procedure (best, exact way)
1. Use a random-number generator that produces a uniform number r in [0,1).
2. Compute p = 1/k.
3. If r < p, record “home run”; otherwise record “not a home run.”

This procedure simulates independent at-bats with the required probability p.

Equivalent integer method (if your generator gives integers 1..k)
1. Generate a random integer X uniformly from 1 to k.
2. If X = 1, record “home run”; otherwise record “not a home run.”

Example: if the player homers once every 20 at-bats, p = 1/20 = 0.05. For each at-bat generate r in [0,1); if r < 0.05 declare a homerun.