lecture07

lecture07 - f(x ) x-5 5 ( 29 = x f Continuous random...

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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
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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
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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 --=-= = dx x f x X E X E X V 2 2 2 ( 29 ( 29 -= = dx x xf X E 2 = 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 -&lt; = b x b x a a b a x x f , , 1 , ( 29 --&lt; = 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 ( 29 ( 29 ( 29 =-= 2 2 X E X E...
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lecture07 - f(x ) x-5 5 ( 29 = x f Continuous random...

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