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NormalFunctions

# NormalFunctions - 2 2 EZ = Var Z = 1 Z = aY b EZ = a b Va...

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Learning Objectives Statethelinear transformation property of normal random Usethelinear transformation property of normal random variables and thecumulativedistribution function of the standard normal to calculateprobabilities of normal randomvariables 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 VarZ [] = a 2 σ 2
“Standardize” Use linear transformation property to standardize a normal RV: Y ~ N ( μ , σ ) Z = Y - μ σ

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“Standardize” Z = Y - μ σ Z = 1 σ Y + - μ σ EZ [] = 1 σ μ + - μ σ VarZ [ ]

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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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