Chapter 6

# Chapter 6 - Chapter 6 Some Continuous Probability...

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Chapter 6. Some Continuous Probability Distributions 6.1 Continuous Uniform Distribution The density function of the continuous uniform random variable X on the interval [, ] A B is 1 ( ; , ) , 0 elsewhere f xAB A x B BA =≤ = The mean and variance of the uniform distribution are 2 A B µ + = and 2 2 () 12 σ =

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6.2 Normal Distribution In 1806 by Gauss “Gaussian Distribution” The density function of the normal random variable X , with mean µ and variance 2 σ , is 2 2 1 () 2 1 ( ; , ) , 2 x fx e x µσ πσ −− =− + 3 3 + 68.26% 99.73% 1. f x is symmetric about . 2. and determine the location and shape of distribution 3. The linear function of normal r.v. X produces also the normal distribution.
1 µ 2 3 1 σ 2 3

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Standard Normal Distribution 2 2 1 () 2 1 ( ) , 0 2 x fx e x µ σ µσ πσ −− =− < < < < > 2 2 2 1 2 1 2 2 ( ) ( ) 1 ~ (0, 1) 2 1 2 11 1 ( ) ( ) ( ) 0 ( ) ( ) 1 x b a b Z a P aXb P Xb P Xa X ed x Z N z E Z E X Var Z Var X π µµ σσ <<= ≤− =⇒ = = = = = =
6.3 Normal Approximation to the Binomial

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Chapter 6 - Chapter 6 Some Continuous Probability...

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