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# Let (X, Y ) be Bivariate Normal, with X and Y marginally N (0, 1) and with correlation

ISBN: 9781466575578 423

## Solution for problem 71 Chapter 7

Introduction to Probability | 1st Edition

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Problem 71

Let (X, Y ) be Bivariate Normal, with X and Y marginally N (0, 1) and with correlation between X and Y . (a) Show that (X + Y,X Y ) is also Bivariate Normal. (b) Find the joint PDF of X + Y and X Y (without using calculus), assuming 1 <

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The Coefficient of Variation: C.V. = S / x(bar) X(bar)  Mean of data Examples: #1 X(bar)  54 ft S  26 ft C.V. = S / x(bar) = 26/54 = .48 or 48% #2 X(bar)  2 hours S  2.7 hours C.V. = 2.7 / 2 = 1.35 NOTICE: the units cancel when you divide the two numbers, therefore the answer does not have units!! Chebyster’s Theorem: For any set of numbers with mean x(bar) and standard deviation, S, atleast (1 – (1/ k^2) x 100%) of those numbers must fall between [x(bar) – kS] and [x(bar) + kS] ________________________________________________________________________ Quartiles: specific values that attempt to divide quantitative data into four equal parts. 1. find median 2. take median of lower half and upper half 3. then you will find the three medians, th

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