STAT-S 300 Lecture Notes - Lecture 10: Randomness
Section 5.1 Notes- Randomness, Probability, and Simulation 9-25-13
• The Idea of Probability
o Chance behavior unpredictable in short run, but has regular and predictable
pattern in long run
o Law of Large Numbers- if we observe more and more repetitions of any chance
process, proportion of times a specific outcome occurs approaches single value
▪ Ex. As # of coin tosses → ∞, P(H) → 0.5
o Probability of any outcome of chance process is number between 0 and 1 that
describes proportion of times the outcome would occur in very long series of
repetitions
▪ Probability of 0- never occur
▪ Probability of 1- always occurs
• Myths About Randomness
o Short run regularity- when we see results from a sample that are unusual and
believe the samples must not have been random
▪ Short run = lots of variation
▪ Long run = less variation
o Law of averages- belief that outcomes of random event even out within a small
sample
▪ Ex. Expecting head after flipping many tails
• Simulation
o Simulation- model that accurately reflects situation
o Done to help understand how chance behavior works
o Performing a Simulation (4-Step Process)
▪ State: What is the question of interest about some chance process?
▪ Plan: Describe how to use a chance device to imitate one repetition of the
process. Explain clearly how to identify the outcomes of the chance
process (label) and what variable to measure (pairs, runs, avg., etc).
▪ Do: Perform many repetitions of the simulation. Show an example of one
and then graph the rest.
▪ Conclude: Use the results of your simulation to answer the question of
interest in context.
o Solution does not prove a claim, just gives evidence for or against claim
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