ECO220Y1 Chapter Notes - Chapter 8: Marginal Distribution, Conditional Probability, Sunk Costs
ECO220
May 2018
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Ch.8: Randomness and Probability
LO 8.1 Random Phenomena and Empirical Probability
Random phenomenon: A phenomenon is random if we know what outcomes could happen, but
not which particular values will happen
• Can't predict the individual outcomes, but can hope to understand characteristics of long-
run behaviour
For any random phenomenon, each trial generates an outcome
Trial: A single attempt or realization of a random phenomenon
Outcome: The value measured, observed, or reported for an individual instance of that trial
Event: A collection/combination of outcomes.
• Usually, we identify events so that we can attach probabilities to them.
• We denote events with bold capital letters such as A, B or C
Sample space: collection of all possible outcomes
• Denote the sample space 'S'
• Has a probability of 1
ECO220
May 2018
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Empirical Probability
Probability: a number between 0 and 1 that reports the likelihood of an event's occurrence. We
write P(A) for the probability of the event A
• Based on repeatedly observing the event's outcome
Empirical probability: when the probability comes from the long-run relative frequency of the
event's occurrence
• The relative frequency of an event's occurrence as the probability of an event
Independence: one event occurring does not change the probability of another
Law of Large Numbers (LLN): long-run relative frequency of repeated, independent events
settles down to the true relative frequency as the number of trials increases
• If the events are independent, then as the number of outcomes increases, the long-run
relative frequency of each outcome gets closer and closer to a single value
• The long-run relative frequency of repeated, independent events eventually hones in on the
empirical probability as the number of trials increases
LO 8.2 The Nonexistent Law of Averages
• Very little is known about the behaviour of random events in the short run
• There is no law of averages for short runs - no Law of Small Numbers
o Belief in such can lead to poor business decisions
LO 8.3 Two More Types of Probability
Model-Based (Theoretical) Probability
• When outcomes are equally likely, their probability is easy to compute. It's just one divided
by the number of possible outcomes
Subjective or Personal Probability
Define probability in two ways:
1. In terms of relative frequency - OR fraction of times that an event occurs in the long run
2. As the number of outcomes in the event divided by the total number of outcomes
Subjective/ Personal probability: a probability that is subjective and represents your personal
degree of belief
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ECO220Y1 Full Course Notes
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Document Summary
Random phenomenon: a phenomenon is random if we know what outcomes could happen, but not which particular values will happen: can"t predict the individual outcomes, but can hope to understand characteristics of long- run behaviour. For any random phenomenon, each trial generates an outcome. Trial: a single attempt or realization of a random phenomenon. Outcome: the value measured, observed, or reported for an individual instance of that trial. Event: a collection/combination of outcomes: usually, we identify events so that we can attach probabilities to them, we denote events with bold capital letters such as a, b or c. Sample space: collection of all possible outcomes: denote the sample space "s, has a probability of 1. Probability: a number between 0 and 1 that reports the likelihood of an event"s occurrence. We write p(a) for the probability of the event a: based on repeatedly observing the event"s outcome.
