Class 08 Functions of random variables

# Class 08 Functions of random variables - Functions of...

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T. R. Willemain MAU Spring06 1 Functions of random variables, including statistics Prof. Tom Willemain

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T. R. Willemain MAU Spring06 2 Agenda Functions of RVs linear/nonlinear functions univariate/multivariate functions independent/dependent RVs Ex: Propagation of error Random samples and statistics (functions) computed from random samples Sample mean Xbar and Central limit theorem Microquiz 08
T. R. Willemain MAU Spring06 3 Linear functions of RVs Linear, univariate Y = a+bX E[Y]=a+bE[X], V[Y]=b 2 V[X] Linear, multivariate, independent Y = a+ΣbiXi E[Y]=a+ΣbiE[Xi], V[Y]= Σ bi 2 V[Xi] Linear, multivariate, dependent Y = a+ΣbiXi but Cov[Xi,Xj] = E{(Xi-E[Xi])(Xj-E[Xj]} ≠ 0 E[Y]=a+ΣbiE[Xi], V[Y]= Σ Σ bibjCov[Xi,Xj]

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T. R. Willemain MAU Spring06 4 Nonlinear functions of RVs Nonlinear, univariate Y = h(X) General solution can be complicated See example on next slide Can always use Monte Carlo If can approximate h(X) by Taylor series
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Class 08 Functions of random variables - Functions of...

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