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Lecture 14 Sum of Random Variables

Lecture 14: Sums of Random Variables. TodayPDF of the Sums of Two Random VectorsMoment Generating Functions (MGFs)MGF of the Sum of Indepent R.V.sRandom Sums of Indepent R.V.sCentral Limit TheoremTomorrowCentral Limit Theorem and ApplicationsThe Chernoff BoundReading Assignment: 6.2-6.8.

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Lecture 14 Sum of Random Variables

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    1. Lecture 14 Sum of Random Variables Last Time Functions of Vectors (Cont.) Transformation of Two Random Variables Expected Value Vectors and Correlation Matrix Gaussian Random Vectors Expected Values of Sums Reading Assignment: Sections 5.6-6.1 and Transform 14 - 1

    2. Lecture 14: Sums of Random Variables Today PDF of the Sums of Two Random Vectors Moment Generating Functions (MGFs) MGF of the Sum of Indepent R.V.s Random Sums of Indepent R.V.s Central Limit Theorem Tomorrow Central Limit Theorem and Applications The Chernoff Bound Reading Assignment: 6.2-6.8

    3. Next Week Sample Mean: Expected Value and Variance Derivation of a R.V. from the Expected Value Point Estimate of Model Parameters Confidence Intervals Reading Assignment: 7.1 - 7.4

    4. Example X: mid term exam score Y: final exam score Z = X+Y

    21. Equal MGF ?same distribution Theorem Let X and Y be two random variables with moment-generating functions FX(s) and FY(s). If for some d > 0, FX(s) = FY(s) for all s, -d<s<d, then X and Y have the same distribution.

    22. Related Concepts Probability Generating Function X: D.R.V. X N Characteristic Function

    25. Section 6.4

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