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STA3032 Chapter 2 Probability

# STA3032 Chapter 2 Probability - Chapter 2 Probability 2.1...

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Chapter 2 Probability 2.1 Definitions of Some Basic Terms Definition: A Statistical Experiment is an experiment that has Two or more outcomes and Uncertainty as to which outcome will be observed. Definition: Probability is the study of uncertainty in a statistical experiment. Definition: S = Sample space is the set of all possible outcomes of a statistical experiment. Definition: An event is any subset of the sample space. Notes: Since S φ and S S, both φ = { } and S are events. φ = { } is called the impossible event and has probability zero, i.e., P( φ ) = 0. S is called the definite event and has probability of 1, i.e., P(S) = 1. Probability of any other event, say A, is between zero and one, i.e., 0 ≤ P(A) ≤ 1 for any event A. Set notation and set algebra, such as , , ∪ ∩ ∈ , and complement ( ' c A A A = = ) are used in defining some events. Definition: Mutually exclusive events: Two events A and B are said to be mutually exclusive (or disjoint) if they cannot occur at the same time, i.e., A B φ = . Definitions of probability: a) Equally likely approach: If an experiment has n(S) equally likely outcomes and an event A has n(A) elements in it then P(A) = n(A) / N(S). b) Relative frequency approach: P(A) is the proportion of times an event A would occur in the long run, if the statistical experiment were repeated over and over again, ( 29 ( ) / lim n P A f n →∞ = . c) Axiomatic Definition: The probability of an event A, P(A), is a number assigned to the event A in such a way that all of the following axioms are satisfied: i. Let S be the sample space. Then, P(S) = 1.

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