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# Ch06 - Chapter 6 Probability 1 6.2 Assigning probabilities...

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1 Probability Chapter 6

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2 6.2 Assigning probabilities to Events Random experiment a random experiment is a process or course of action, whose outcome is uncertain. Examples Experiment Outcomes Flip a coin Heads and Tails Record a statistics test marks Numbers between 0 and 100 Measure the time to assemble numbers from zero and above a computer
3 6.2 Assigning probabilities to Events Performing the same random experiment repeatedly, may result in different outcomes, therefore, the best we can do is consider the probability of occurrence of a certain outcome. To determine the probabilities we need to define and list the possible outcomes first.

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4 Determining the outcomes. Build an exhaustive list of all possible outcomes. Make sure the listed outcomes are mutually exclusive. A list of outcomes that meets the two conditions above is called a sample space. Sample Space
5 Sample Space: S = {O 1 , O 2 , …,O k } Sample Space a sample space of a random experiment is a list of all possible outcomes of the experiment. The outcomes must be mutually exclusive and exhaustive. Simple Events The individual outcomes are called simple events . Simple events cannot be further decomposed into constituent outcomes. Event An event is any collection of one or more simple events Our objective is to determine P( A ), the probability that event A will occur. O 1 O 2

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6 – Given a sample space S={ O 1 ,O 2 ,…,O k }, the following characteristics for the probability P( O i ) of the simple event O i must hold: Probability of an event: The probability P( A ) of event A is the sum of the ( 29 ( 29 = = k i i i O P i each for O P 1 1 . 2 1 0 . 1 Assigning Probabilities
7 Approaches to Assigning Probabilities and Interpretation of Probability Approaches The classical approach The relative frequency approach The subjective approach Interpretation If a random experiment is repeated an infinite number of times, the relative frequency for any given outcome is the probability of this outcome.

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8 6.3 Joint, Marginal, and Conditional Probability We study methods to determine probabilities of events that result from combining other events in various ways. There are several types of combinations and relationships between events: Intersection of events Union of events Dependent and independent events Complement event
9 Intersection The intersection of event A and B is the event that occurs when both A and B occur. The intersection of events A and B is denoted by (A and B). The joint probability of A and B is the probability of the intersection of A and B, which is denoted by P(A and B)

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10 Example 6.1 A potential investor examined the relationship between the performance of mutual funds and the school the fund manager earned his/her MBA.
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Ch06 - Chapter 6 Probability 1 6.2 Assigning probabilities...

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