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Statistics (133)
STAB22H3 (130)
Chapter 14

Chapter 14.docx

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University of Toronto Scarborough
Mahinda Samarakoon

Stats: Data and Models – Canadian Edition Chapter 14 – From Randomness to Probability Empirically Probability - Trial – each occasion upon which we observe a random phenomenon - The trial’s outcome is the value of the random phenomenon at each trial - Event – a combination of outcomes (i.e. treating a yellow light like a red or green light), but individual outcomes not combined with anything else are also events - Sample space – the collection of all possible outcomes The Law of Large Numbers - If we assume events are independent, the outcome of one trial doesn’t affect the outcomes of others - (LLN) as the number of trials increases, the long-run relative frequency of repeated events gets closer and closer to a single value, called the probability of an event - Empirical probability – repeatedly observing the event’s outcome - For an event (A), the relative frequency of (A) = # of times A occurs/total # of trials The Nonexistent Law of Averages - Law of Averages – the belief that an outcome of a random event that hasn’t occurred in many trials is “due” to occur - The LLN says nothing about short-term behaviour - Sequences of random events don’t compensate in the short run and don’t need to do so to get back to the right long-run probability Theoretical Probability - When outcomes are equally likely, their probability is easy to compute - The probability of the event is the number of outcomes in the event divided by the total number of possible outcomes o P(A) = # outcomes in A/ # of possible outcomes Personal Probability - Personal/subjective proba
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