Surveys, Experiments, and Simulations Unit 3 Part 4 Simulations

Why Simulate? To gain a better understanding of the nature of randomness and probability. To make predictions. To save time. The Purpose of Simulations

Real Life Simulations: Weather and Hurricane Forcasting / Modeling The Purpose of Simulations

Real Life Simulations: Stock Market Analysis The Purpose of Simulations

Real Life Simulations: Earthquake and Tsunami Predictions The Purpose of Simulations

Long Term Expected Average A classic example used to explain long term expected average is a simple coin flip. We know the probability of heads P(Heads) to be 50%. So we expect 50% of our total flips to turn out heads. In the short run, it is perfectly reasonable to deviate far from the expected 50% average, however, we expect, in the long run to approach 50% heads. This is, in fact, the definition of random: Short term unknowable frequency with a long term expected frequency. Long Term Expected Average and the Gambler’s Fallacy

Long Term Expected Average Here is a plot against number of flips demonstrating initial high degree of variability with a long term approach towards the expected 50%. Long Term Expected Average and the Gambler’s Fallacy

The Gambler’s Fallacy Humans are hard wired to expect a “regression towards the mean” – however, we typically don’t have a good understanding of what “long term” really means. Red, Black, Black, Black, Black, Black, Black, _____ When a gambler sees the above history of events on the roulette wheel, they think the next event will either be Black because “Black is on a run” or Red because “Red is due.” In reality, neither is the case. The roulette wheel has no memory and the events are independent. The next spin has an equal probability of being red or black. Long Term Expected Average and the Gambler’s Fallacy

Conducting Simple Simulations Using a calculator you can conduct simple simulations. Ex.1: “Simulate 20 flips of a fair coin.” Steps: Math -> PRB -> RandomInt(0,1,20) Note: Assign the values to events like so – 0 = Heads 1 = Tails Simulations

Conducting Simple Simulations Ex.2: “A basketball player has a 45% chance to make a shot. Simulate 10 shots.” Steps: Math -> PRB -> RandomInt(1,100,10) Note: Assign the values to events like so – 1-45 = Make = Miss Simulations