STATISTICS 1

STATISTICS 1

1. FUNCTION OF RANDOM VARIABLE

   • METHOD OF DISTRIBUTION FUNTIONS
     • CDF Method
       • A FUNCTION OF RANDOM VARIABLE
         • ASSUMPTIONS
           • X is continuous random variable with known PDF
           • g is real-valued function defined and differentiable in the range X
         • PROCEDURES
           • Identify range of Y
           • Find derivative of CDF of Y
           • PDF of Y
             • f(y)=F(y), derivative exist
             • f(y)=0, otherwise
           • Determine CDF of Y in terms of X
           • Identify PDF of X
       • FUNCTION OF JOINTLY DISTRIBUTED RANDOM VARIABLE
         • PROCEDURES
   • METHOD OF MOMENT-GENERATING FUNCTIONS
     • DEFINITION
       • MACLAURIN SERIES
       • TAYLOR SERIES
     • PROPERTIES
     • THEOREM
     • GENERATING MOMENT FROM MGF
     • JOINT MGF
       • THEOREM
       • PROOF
   • METHOD OF TRANSFORMATION
     • UNIVARIATE
       • THEOREM
       • ASSUMPTIONS
         • X is continuous random variable with known PDF
         • g is real-valued function defined and differentiable in the range X
       • PROCEDURES
         • Identify range of Y
         • Apply .
         • For y in the range of Y, solve x in y=g(x)
         • Use step 2-4 to get PDF of Y
         • Identify the PDF of X and range of X whether satisfies the theorem
     • BIVARIATE
       • THEOREM
         • JACOBIAN DETERMINANT OF THE TRANSFORMATION

2. RANDOM VARIABLE

   • DISCRETE PROBABILITY DISTRIBUTION
     • BERNOULLI DISTRIBUTION
   • CONTINUOUS PROBABILITY DENSITY FUNCTION
     • CHI-SQUARE DISTRIBUTION
     • GAMMA DISTRIBUTION
     • BETA DISTRIBUTION
       • A continuous family on (0,1)
       • To model proportion

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