NormalFunctions - 2 2 EZ = Var Z = 1 Z = aY b EZ = a b Va rZ = a 2 2 linear transformation property Use Φ(y PX< x 29 = P X-μ σ< x-μ Y =

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Learning Objectives State the linear transformation property of normal random Use the linear transformation property of normal random variables and the cumulative distribution function of the standard normal to calculate probabilities of normal random variables of arbitr .
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Linear Transformation If Y ~ N( μ , σ ) and Z is a linear transformation: then Z is also normal and Z = aY + b EZ [] = a μ + b Va rZ [] = a 2 σ 2
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“Standardize” Use linear transformation property to standardize a normal RV: Y ~ N ( μ , σ ) Z = Y
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“Standardize” Z = Y σ Z = 1 Y + EZ [] = 1 μ + VarZ [ ] = 1
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Unformatted text preview: 2 2 EZ = Var Z = 1 Z = aY + b EZ = a + b Va rZ = a 2 2 linear transformation property Use Φ (y) PX < x ( 29 = P X-μ σ < x-μ Y = X-μ PX < x ( 29 = PY < x-μ PX < x ( 29 =Φ x-μ PX < x ( 29 Y ~ no rm a l (0 ,1 ) Exercises • Exercise #0 • Exercise #1 • Exercise #2 • Exercise #3 • Exercise #4 • Exercise #5 • Exercise #6 • Exercise #7 • Exercise #8 • Exercise #9...
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This note was uploaded on 02/22/2010 for the course BME 335 taught by Professor Dunn during the Spring '10 term at University of Texas at Austin.

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NormalFunctions - 2 2 EZ = Var Z = 1 Z = aY b EZ = a b Va rZ = a 2 2 linear transformation property Use Φ(y PX< x 29 = P X-μ σ< x-μ Y =

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