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8. For the RV (X, Y) the joint PDF is given as if 0 ≤ x, y ≤ 2 (a) fx,y (x, y): 0 elsewhere Find for (a) and (b), (i) P{X ≤ 1,Y ≤ 1} (ii) P {X+Y ≤ 1} (iii) P {X + Y > 2} (iv) P {X ≤ 2Y} (v) P {X> 1} (vi) P{X = Y} (vii) P {Y> 1 X ≤ 1} (viii) P {X>Y|Y> 1}. (b) fx,y (x, y) = e-(x+y) if x ≥ 0, y ≥0 elsewhere To

8. For the RV (X, Y) the joint PDF is given as if 0 ≤ x, y ≤ 2 (a) fx,y (x, y): 0 elsewhere Find for (a) and (b), (i) P{X ≤ 1,Y ≤ 1} (ii) P {X+Y ≤ 1} (iii) P {X + Y > 2} (iv) P {X ≤ 2Y} (v) P {X> 1} (vi) P{X = Y} (vii) P {Y> 1 X ≤ 1} (viii) P {X>Y|Y> 1}. (b) fx,y (x, y) = e-(x+y) if x ≥ 0, y ≥0 elsewhere To

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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8. For the RV (X, Y) the joint PDF is given as if 0 ≤ x, y ≤ 2 elsewhere (a) fx,y (x, y) = 4 Je-(x+y) if x ≥ 0, y 20 { elsewhere (b) fx,y (x, y) = Find for (a) and (b), (i) P {X ≤ 1, Y ≤ 1} (ii) P {X + Y ≤ 1} (iii) P {X + Y > 2} (iv) P {X ≤ 2Y} (v) P{X > 1} (vi) P {X = Y} (vii) P {Y > 1| X ≤ 1} (viii) P{X > Y|Y> 1}.
Transcribed Image Text:8. For the RV (X, Y) the joint PDF is given as if 0 ≤ x, y ≤ 2 elsewhere (a) fx,y (x, y) = 4 Je-(x+y) if x ≥ 0, y 20 { elsewhere (b) fx,y (x, y) = Find for (a) and (b), (i) P {X ≤ 1, Y ≤ 1} (ii) P {X + Y ≤ 1} (iii) P {X + Y > 2} (iv) P {X ≤ 2Y} (v) P{X > 1} (vi) P {X = Y} (vii) P {Y > 1| X ≤ 1} (viii) P{X > Y|Y> 1}.
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