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Unformatted text preview: Transformation • Let X ∼ N ( μ,σ 2 ), so it has density f ( x ) = 1 √ 2 πσ 2 exp ( x μ ) 2 2 σ 2 ! . Can you tell me the distribution of X μ σ ? or in other words, what is its density? 1 One application of zscore • In many applications, the normal distribu tions usually have different means and vari ances. Suppose you have the probabil ity table for the standard normal random variable, is it possible for you to compute P ( X ≤ x ) for X ∼ N (2 , 4) and x = 1 . 6? • Application: midterm and final. 2 Sample problem • Problem : Assume that the length of time, X , between the charges of a cellular phone is normally distributed with a mean of 10 hours and a standard deviation of 1.5 hours. Find the probability that the cell phone will last between 8 and 12 hours between charges. 3 Discrete vs Continuous • One obvious difference is the interpreta tion of P ( X = x ). It is totally meaningful for discrete, but not so much for continu ous random variables. For continuous, it’s usually zero, so the density is not given by the notation P ( X...
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This note was uploaded on 06/06/2011 for the course STAT 515 taught by Professor Zhao during the Spring '10 term at South Carolina.
 Spring '10
 Zhao
 Normal Distribution

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