Let the r.v.s X and Y have the Bivariate normal distribution with parameters μ 1 , μ
Question:
Where
(i) Show that the exponent may be written thus:
Where b = m2 + rs2/s1 (x m1)
(ii) From part (i), it follows that:
From this expression, and without any actual integration, conclude that the r.v. X is distributed as N (m1, s21); i.e., X ~ N (μ1, s21), and by symmetry, Y ~ N (m2, s22).
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Related Book For
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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