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ECON 2B03 (45)
Lecture 8

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Jeff Racine

Random event Simple event Composite event Ask two people if interest rates are going up They must answer “yes” or “no” Simple events: a1 = (Y,Y), a2 = (Y,N), How Random Events Relate Complementary events Two random event for which all basic outcomes not contained in one event are A contained in the other event (denoted A and , the bar denoting ‘complementary’) Such events are both mutually exclusive and collectively exhaustive at the same time Unions of Events (logical operator U [or]) All basic outcomes contained in one or the other event ∩ Intersections of Events (logical operator [and]) All basic outcomes contained in one and the other event Probability Concepts Objective Probability: The theoretical Approach Relies entirely on abstract reasoning Logic provides all answers The probability of an event A: p(A)= n N Here, n is the number of equally likely basic outcomes that are favorable to the occurrence of event A, while N is the total number of equally likely basic outcomes possible Example (Objective Probability) An unbiased die has 6 faces ({1,2,3,4,5,6}), each equally likely. Hence the theoretical probability of obtaining the face ‘1’ in one toss of the die is 1/6 = 0.166667 Objective Probability: The Empirical Approach Probability values are derived from dta, i.e. experience The probability of an event is equal to the relative frequency with which it has actually been observed in the past The probability of an event A: k p(A)= M Here, k is the number of times A occurred in the past during a large number of random experiments, while M is the maximum number of times A could have occurred Example Roll a die, say, M = 60,000 times and record each outcome. If there were An alternative to objectively obtained probabilities can be found in the notion ‘subjective probability’ Subjective Probability Purely personal beliefs in the degree of likelihood that some event will occur Hunches people have, e.g., The likelihood of a recession this year The likelihood of oil being found at a given site Counting Techniques Factorials: Let n be a positive integer. The product of all integers from 1 to n is called ‘n factorial’, and is denoted as n! = n x ( n -1) x (n-2) x
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