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A particle moves within the region A bounded by the positive x axis and the positive...

A particle moves within the region A bounded by the positive x axis and the positive part of line y=x. Let (X,Y) denote the position of the particle at a given time. The joint probability density of X and Y is given by

fX,Y (x, y)=2e^-(x+y) for (x, y) 2 A

(i) Are X and Y independent?

(ii) Find the marginal probability density function of X.

(iii) Conditioned on X=0.4, find the probability 0.3 < Y < 0.6

Math   Statistics-And-Probability   
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