Statistics / Unit 7: Random Variables
7.6 Simulation
Notes
A simulation uses random numbers to imitate a random process, so probabilities can be estimated when direct calculation is hard.
- Steps: (1) state the model and assign digits to outcomes, (2) simulate one trial, (3) record the result, (4) repeat many times, (5) estimate the probability as $\displaystyle \frac{\text{number of successes}}{\text{number of trials}}$.
- Digits must match the probability. For $P = 0.4$ using digits 0 to 9, use four digits (such as 0 to 3).
- More repetitions give estimates closer to the true probability (law of large numbers).
- Example: In 50 trials the event occurred 14 times, so the estimate is $\displaystyle \frac{14}{50} = 0.28$.
Practice
A basketball player makes $40\%$ of her shots. Using random digits 0 to 9, which assignment simulates one shot?
Four of the ten digits give a probability of $0.4$.
A simulation of 50 trials had the event occur 14 times. The estimated probability is:
$\displaystyle \frac{14}{50} = 0.28$.
Why should a simulation be repeated many times?
Relative frequency settles near the true probability in the long run.
Ready for more? Take the Unit 7 test.