# Lecture 6 - Chapter6 Continuous Distributions...

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Chapter 6 Continuous Continuous Distributions Distributions

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Learning Objectives Calculate expected value and variance of linear  combinations of random variables Understand concepts of the uniform distribution Appreciate the importance of the normal  distribution Recognise problems involving the normal  distribution and be able to solve such problems Be able to use  the normal distribution to  approximate binomial distribution problems, and  know how to solve such problems
Transformed  Random Variables Often there is a need to  transform  random variables, e.g.  convert A\$ to US\$. What is the expected value of Y? c aX Y + =

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We sometimes construct a random variable as a linear  combination of two other RVs What is the expected value of Q? Expected Value of Transformed  Random Variables c bY aX Q + + =
Expected Value of Two RVs -  Example Let Q = 2X - 3Y + 6, E(X) = 4, E(Y) = 5 Find E(Q)

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Variance of Transformed  Random Variables Variance of  Y=aX+c  is Variance of  Q=aX+bY+c  is ) , ( 2 ) ( ) ( ) ( 2 2 Y X abCov Y V b X V a Q V + + = ) ( ) ( 2 X V a Y V =
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## This note was uploaded on 08/22/2011 for the course FINC 2011 taught by Professor Craigmellare during the Three '10 term at University of Sydney.

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Lecture 6 - Chapter6 Continuous Distributions...

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