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Chapter 4

# Chapter 4

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University of Toronto Scarborough

Statistics

STAB22H3

Moras

Winter

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Chapter 4 4.1 Randomness Probability - a pattern that emerges clearly only after many repetitions. The proportion of times the outcome will occur in a long series of repetitions. 4.1 Toss a coin 5000 times. Probability describes only what happens in the long run. (repetitive trials) The language of probability Random in statistics is a kind of order that emerges in the long run. Randomness and probability Random when the individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions Probability (random) repetitive trials (look at overall picture) Fair has equally likely chances Ex: Fair Coin = head and tail sides Thinking about randomness - Long series of independent trials - Observing many trials (done practically) - Simulations useful when a lot trials are down without being practical The uses of probability Games of chance Ex: dice, cards, or spinning a roulette wheel, gambling Job wise Ex: astronomy, 4.2 Probability Models Probability model description of random phenomenon in the language of mathematics Description of probability outcomes (probability model): - A list of possible outcomes - A probability for each outcome Sample Space The sample Space (S) of a random phenomenon is the set of all possible outcomes. - Each possible outcome is a sample and the sample space contains all possible samples. www.notesolution.com

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