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Unformatted text preview: Administration CS70: Satish Rao: Lecture 31. Continuous Probability 1. Review Continuous Probability. 2. Exponential Distribution. 3. Normal (Gaussian) Distribution. 4. Central Limit Theorem. Continuous Probability is continuous space. Continuous Probability is continuous space. Probability of any outcome is 0. Continuous Probability is continuous space. Probability of any outcome is 0. Work with events. Continuous Probability is continuous space. Probability of any outcome is 0. Work with events. Example: James Bond lands on position uniformly [ , 1000 ] . Continuous Probability is continuous space. Probability of any outcome is 0. Work with events. Example: James Bond lands on position uniformly [ , 1000 ] . Probability lands in an interval [ a , b ] [ , 1000 ] is Continuous Probability is continuous space. Probability of any outcome is 0. Work with events. Example: James Bond lands on position uniformly [ , 1000 ] . Probability lands in an interval [ a , b ] [ , 1000 ] is b a 1000 . Random Variables Continuous random variable X , specified by 1. F ( x ) = Pr [ X x ] for all x . Random Variables Continuous random variable X , specified by 1. F ( x ) = Pr [ X x ] for all x . Cumulutive Distribution Function (cdf) . Random Variables Continuous random variable X , specified by 1. F ( x ) = Pr [ X x ] for all x . Cumulutive Distribution Function (cdf) . Pr [ a X b ] = F ( b ) F ( a ) Random Variables Continuous random variable X , specified by 1. F ( x ) = Pr [ X x ] for all x . Cumulutive Distribution Function (cdf) . Pr [ a X b ] = F ( b ) F ( a ) 1.1 F ( x ) 1 for all x . 1.2 F ( x ) F ( y ) if x y . 2. or f ( x ) , where F ( x ) = R  f ( x ) or f ( x ) = d ( F ( x )) dx . Random Variables Continuous random variable X , specified by 1. F ( x ) = Pr [ X x ] for all x . Cumulutive Distribution Function (cdf) . Pr [ a X b ] = F ( b ) F ( a ) 1.1 F ( x ) 1 for all x . 1.2 F ( x ) F ( y ) if x y . 2. or f ( x ) , where F ( x ) = R  f ( x ) or f ( x ) = d ( F ( x )) dx . Probability Density Function. Random Variables Continuous random variable X , specified by 1. F ( x ) = Pr [ X x ] for all x . Cumulutive Distribution Function (cdf) . Pr [ a X b ] = F ( b ) F ( a ) 1.1 F ( x ) 1 for all x . 1.2 F ( x ) F ( y ) if x y . 2. or f ( x ) , where F ( x ) = R  f ( x ) or f ( x ) = d ( F ( x )) dx . Probability Density Function. Pr [ a X b ] = R b a f ( x ) d ( x ) Random Variables Continuous random variable X , specified by 1. F ( x ) = Pr [ X x ] for all x . Cumulutive Distribution Function (cdf) ....
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This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.
 Fall '11
 Rau

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