20065ee131A_1_EE131AF06HW7

20065ee131A_1_EE131AF06HW7 - Problem 3 The random vector X...

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Assignment 7, EE 131A Due: Monday December 4, 2006 Problem 1. For the two-dimensional random variable ( X,Y ) sketch the region of the plane corresponding to the following events. (a) { X - Y 1 } . (b) { max( X,Y ) < 2 } . (c) {| X - Y | ≤ 2 } . (d) {| X | < | Y |} . (e) { X 2 Y } . (f) { max( | X | , | Y | ) < 2 } Problem 2. The joint density function of X and Y is given by f X,Y ( x,y ) = c ( y - x ) e - y , if - y < x < y and 0 < y < , 0 elsewhere.
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Unformatted text preview: Problem 3. The random vector ( X, Y ) has a joint pdf f X,Y ( x, y ) = 2 e-x e-2 y if x > and y > , elsewhere. Find the probabilities of the following events: (a) { X + Y ≤ 8 } . (b) { X < Y } . (c) { X-Y ≤ 2 } . (d) { X 2 < Y } . ( Hint: The evaluation of (d) involves the cdf of the standard normal random variable.)...
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  • Spring '08
  • LORENZELLI
  • Probability theory, probability density function, Cumulative distribution function, normal random variable, joint density function, following events

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