lecture7 - Transformation • Let X ∼ N μ,σ 2 so it has...

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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 z-score • 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.

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lecture7 - Transformation • Let X ∼ N μ,σ 2 so it has...

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