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Chapter 14

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University of Toronto Scarborough

Statistics

STAB22H3

Mahinda Samarakoon

Winter

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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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