Suppose that X and Y are jointly normal, i.e. they have the joint PDF: (a) Derive the
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Suppose that X and Y are jointly normal, i.e. they have the joint PDF:
(a) Derive the marginal distribution of X and Y and observe that both are normal distributions.
(b) Derive the conditional distribution of Y given X Æ x. Observe that it is also a normal distribution.
(c) Derive the joint distribution of (X,Z) where Z Æ (Y /¾Y )¡(½X/¾X ), and then show that X and Z are independent.
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