# solution11 - 1 SOLUTION Probability for Engineering...

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1 SOLUTION Probability for Engineering Applications Assignment #11 1. (3 pt) For the two-dimensional random variable Z= (X,Y) sketch the region of the plane corresponding to the following events and state whether the events are in product form. (cf. Problem 4.1) 1a. {(X-Y) 3} 1b. {e X < 3} 1c. {|X – Y| < 3} 1d. {min (X,Y) < 3} 1e. {|X| < |Y|} 1f. {X/Y < 3} 1g. {X 2 < Y} 1h. {XY < 3} 1i. {max (|X|,|Y|) < 3} 1j. {X > -3} 1a 1b . X-Y < 3 (NOT in product form) X < ln 3 (product form) 3 X Y 3 3 X Y 3

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2 1c. 1d. |X-Y| < 3 (NOT in product form) min(X,Y) < 3 (NOT in product form) 1e. 1f. |X|<|Y| (NOT) X/Y < 3 (NOT) 1g. 1h. X 2 < Y (NOT in product form) XY < 3 (NOT) 1i. 1j. max(|X|,|Y|) < 3 (product form) X > -3 (product form) 3 X Y 3 3 X Y 3 3 X Y 3 3 X Y 3 3 X Y 3 3 X Y 3 3 X Y 3 3 X Y 3
3 2. (3 pts) X and Y have the joint pmf indicated in the table below. (cf. Problem 4.5) Y -1 0 +1 -1 0.10 0.05 0.10 0 0.05 0.15 0.15 X +1 0.25 0.10 0.05 2a. P[X=0] = 0.05 + 0.15 + 0.15 = 0.35 2b. F X (1)

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## This note was uploaded on 09/03/2008 for the course ECSE 4510 taught by Professor Woods during the Spring '03 term at Rensselaer Polytechnic Institute.

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solution11 - 1 SOLUTION Probability for Engineering...

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