Unformatted text preview: X 1 X 1 + X 2 . (Name it!) 8. Let X 1 and X 2 have the joint pdf f X 1 ,X 2 ( x 1 , x 2 ) = 2 ex 1x 2 I (0 ,x 2 ) ( x 1 ) I (0 , ∞ ) ( x 2 ) . (a) Find the marginal pdfs for X 1 and X 2 . (b) Suppose that Y 1 = 2 X 1 and Y 2 = X 2X 1 . Show that Y 1 and Y 2 are independent. 9. Required for 5520 students only: Suppose that X is a continuous random variable with pdf f ( x ). Let Y = X 2 . (Note that this is not a onetoone, invertible transformation.) Find an expression for the pdf of Y in terms of the pdf of X ....
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 Fall '11
 Manuel
 Probability distribution, Probability theory, probability density function, Cumulative distribution function, Discrete probability distribution, iid X1 X1

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