Final Exam Review Questions - Final Exam Review 7:00-9:00pm...

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Final Exam Review 7:00-9:00pm, Dec 17; Willard 62 You can bring two double-sided cheating sheets and a calculator with you in the exam. The exam is comprehensive, consisting of five written problems. But Chapter 3-5 will be the emphasis. Please go through all examples discussed in class and the homework problems. The cumulative Binomial, Poisson and Standard Normal probability tables will be provided. Testing Points: For both Discrete and Continuous r.v.: Joint and marginal probability mass function/density Cumulative Distribution Function (CDF): F ( x ) = P ( X x ) = ( y : y x p ( y ) R x -∞ f ( y ) dy Expected Value: E ( X ) = μ x = ( x D x · p ( x ) R -∞ x · f ( x ) dx Variance: V ( X ) = E [( X - μ ) 2 ] = E ( X 2 ) - ( EX ) 2 Moment Generating Function (MGF): M X ( t ) = E ( e tX ) = ( x D e tx · p ( x ) R -∞ e tx · f ( x ) dx 1
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Conditional PMF/density p Y | X ( y | x ) = p ( x, y ) p X ( x ) f Y | X ( y | x ) = f ( x, y ) f X ( x ) Conditional mean and variance Covariance Cov ( X, Y ) = E [( X - μ X )( Y - μ Y )] = ( x y ( x - μ X )( y - μ Y ) p ( x, y ) R -∞
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