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Let X and Y be a continuous random variables defined on the probability space (,E(),P). If the density function of X is defined by: fXY(x,y)={Ae(x+y),0,0yx,x<otherwise where A>0 is a constant. 1. (5pts) Find the constant A. 2. (10pts) Find the distribution and the density function for X. 3. (5pts) Compute the probability P[X<2,1<Y]. 4. (5pts) Compute the conditional probability P[X4X>3] . 5. (10pts) Compute the expected value, E[XY]..

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Let X and Y be a continuous random variables defined on the probability space (,E(),P). If the density function of X is defined by: fXY(x,y)={Ae(x+y),0,0yx,x<otherwise where A>0 is a constant. 1. (5pts) Find the constant A. 2. (10pts) Find the distribution and the density function for X. 3. (5pts) Compute the probability P[X<2,1<Y]. 4. (5pts) Compute the conditional probability P[X4X>3] . 5. (10pts) Compute the expected value, E[XY].

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Let X and Y be a continuous random variables defined on the .pdf

  • 1. Let X and Y be a continuous random variables defined on the probability space (,E(),P). If the density function of X is defined by: fXY(x,y)={Ae(x+y),0,0yx,x<otherwise where A>0 is a constant. 1. (5pts) Find the constant A. 2. (10pts) Find the distribution and the density function for X. 3. (5pts) Compute the probability P[X<2,1<Y]. 4. (5pts) Compute the conditional probability P[X4X>3] . 5. (10pts) Compute the expected value, E[XY].