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lecture07

# lecture07 - f(x x-5 5 29 = x f Continuous random variable...

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Cumulative Distribution Function (CDF) Definition Example Roulette, straight bet ( 29 ( 29 x X P x F = x (in dollar) -1 35 p(x) 36/37 1/37 ( 29 < - - < = 35 , 1 35 1 , 37 / 36 1 , 0 x x x x F

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Cumulative Distribution Function (CDF) Example Even money bet: bet \$1 on even numbers x (in dollar) -1 1 p(x) ( 29 = x F F(x) x -1 -1
Continuous random variables Example: The height (weight) of a randomly selected person Measurements of temperature, pH, electric current, etc.

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Probability density function Properties: ( 29 x x f 2200 , 0 ( 29 - = 1 dx x f
Probability density function ( 29 ( 29 = < < b a dx x f b X a P

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Continuous random variable Example Class starts at 8:00 AM. The professor may arrive at any moment between 7:55 to 8:05. Let X be the number of minutes by which the professor arrives later than 8:00 (If he/she arrives earlier than 8:00, then X is negative.)

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Unformatted text preview: f(x ) x-5 5 ( 29 = x f Continuous random variable Mean, variance, and standard deviation ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 âˆ« âˆž âˆž--=-= = dx x f x X E X E X V 2 2 2 Î¼ Ïƒ ( 29 ( 29 âˆ« âˆž âˆž-= = dx x xf X E 2 Ïƒ= Uniform distribution Definition A distribution such that for each member of the family, all intervals of the same length on the distribution's support are equally probable X~U(a,b) ( 29 â‰¤ â‰¤-< = b x b x a a b a x x f , , 1 , ( 29 â‰¤ â‰¤--< = b x b x a a b a x a x x F , 1 , , Uniform distribution Uniform distribution X~U(a,b) ( 29 = = X E Î¼ ( 29 ( 29 ( 29 =-= 2 2 X E X E Ïƒ...
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lecture07 - f(x x-5 5 29 = x f Continuous random variable...

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