Week_8_Slides - Week 8 Finding Distribution Functions of...

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Week 8 Finding Distribution Functions of Functions of R.V.’s Mixture and Mixed Distributions Normal Distribution Theory
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Recap Functions of R.V.’s Statisticians – statistics of interest such as sample mean and variance Finance – portfolio construction, derivative pricing Physics – molecular speeds of gases – Maxwell-Boltzmann Distribution
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Statistics
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Finance
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Atoms or Molecules Move Randomly is distributed as Z follows a Maxwell–Boltzmann distribution with parameter a .
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Methods for finding PDF’s for Functions of R.V.’s Find CDF first Find PDF directly Use MGF When to use which method? What functions will allow us to use the transformation method? How do we find the distribution of multiple functions of multiple random variables?
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Jacobian Matrix and Determinant Suppose that Y = ( 1 ,..., n Y Y ) is a vector of continuous random variables with joint pdf f ( y ) = 1 ( ,..., ) n f y y , and 1 ( ,..., ) i i n x g y y , i = 1,. .., n
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Week_8_Slides - Week 8 Finding Distribution Functions of...

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