W6-slides1 - f Y ( t ) dt = Z y a 1 b-a dt = y-a b-a If y 1...

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Lecture 16- Outline and Examples Continuous random variables (Ross Ch 5) -Uniform random varibale (Ross § 5.3) -Normal (Gaussian) random variable (Ross § 5.4)
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Uniform random variables (Ross § 5.3) The uniform distribution on ( a , b ). Write: Y U ( a , b ). f Y ( y ) = ± 1 b - a a < y < b 0 otherwise
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Example. Let Y be uniform (0, 2) distribution. Find the probability that Y is 1.23 correct to two decimal places. Solution. The pdf is f ( x ) = 1 / 2 for x (0 , 2) and 0 otherwise. P (1 . 225 < Y < 1 . 235) = Z 1 . 235 1 . 225 1 2 dx = 1 . 235 - 1 . 225 2 = 0 . 005
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Example. Find the cdf F Y of the uniform ( a , b ) distribution. Solution. If y < a then, P ( Y y ) = R y -∞ 0 dt = 0 If a y < b we compute P ( Y y ) = Z y -∞
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Unformatted text preview: f Y ( t ) dt = Z y a 1 b-a dt = y-a b-a If y 1 then P ( Y y ) = R y- f Y ( t ) dt = R b a 1 b-a dt = 1 To summarize: F Y ( y ) = y a y-a b-a a y < b 1 y b Normal random variable Denition: If the pdf of a continuous random variable X is given by f X ( x ) = 1 2 exp "-1 2 x- 2 # , for- < x < , then X is said to have a normal distribution with parameters and , and we write X N ( , 2 )....
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This note was uploaded on 06/05/2010 for the course STAT PStat 120a taught by Professor Rohinikumar during the Spring '10 term at UCSB.

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W6-slides1 - f Y ( t ) dt = Z y a 1 b-a dt = y-a b-a If y 1...

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