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lecture5 - Psych 100A Winter 2010 Lecture 5 Ideas of...

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Psych 100A Winter 2010 Lecture 5: Ideas of Probability and distribution 1.Three definitions 2 Basic concepts 2.Basic concepts 3.Adding probabilities 4.Observed (empirical) versus Theoretical (population) distributions 5.Binomial distribution 6 Normal distribution 6.Normal distribution
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1. Probabilities – What are the chances? Mathematicians have developed several careful and rigorous theories of probability. Cl i l b bilit Classical probability Relative frequency concept of probability Subjective/personal probability
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a. Classical probability Definition . If a random experiment can result in n possible mutually exclusive and equally likely outcomes and if n A of these outcomes have an attribute A, then the probability (Pr) of A is written as n A A ) Pr( n Attribute A is a collection of outcomes and is Concept . This definition is most often called an event. associated with games of chance.
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Example of classical probability: Suppose a card is d t d f di d k f l i drawn at random from an ordinary deck of playing cards. The probability of drawing a diamond (A) is % 25 52 13 ) Pr( n n A A The probability of drawing a number between 5 and 10 inclusive (B) is 10, inclusive (B) is % 46 24 ) P ( n B B 52 Pr( n
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b. Relative frequencies Definition . If an experiment is perfomred n times and if n A of these result in the outcome A then the probability of A outcome A, then the probability of A occurring is defined as the limiting ratio: n n A A n lim ) Pr( Concept . This is an empirical approach to probability that says approximately what percent of the time an event will occur when the basic process is repeated over and over again independently and under the same again, independently and under the same conditions.
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