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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 Ω is continuous space. Continuous Probability Ω is continuous space. Probability of any outcome is 0. Continuous Probability Ω is continuous space. Probability of any outcome is 0. Work with events. Continuous Probability Ω is continuous space. Probability of any outcome is 0. Work with events. Example: James Bond lands on position uniformly [ , 1000 ] . Continuous Probability Ω 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 Ω 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 ∈ ℜ . 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 ∈ ℜ . 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 ∈ ℜ . 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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 Fall '11
 Rau
 Normal Distribution, Variance, Probability theory, probability density function

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