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Let X and Y be two continuous random variables with probability dens.pdf

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Let X and Y be two continuous random variables with probability density functions fX (x) and fY (y). (a) Determine an expression for the density of their difference, fXY , if X and Y are independent. (b) Use your expression to compute the density for X Y for X Unif[0, 1] and Y Unif[0,1]. (c) What is the density of the sum X+Y for XUnif [0,1] and Y Unif [0,1]? (d) How are the answers to parts (b) and (c) similar? What assumptions on X and Y make this so? Prove your observation is true by manipulating your expression in part (a). Solution.

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Let X and Y be two continuous random variables with probability density functions fX (x) and fY (y). (a) Determine an expression for the density of their difference, fXY , if X and Y are independent. (b) Use your expression to compute the density for X Y for X Unif[0, 1] and Y Unif[0,1]. (c) What is the density of the sum X+Y for XUnif [0,1] and Y Unif [0,1]? (d) How are the answers to parts (b) and (c) similar? What assumptions on X and Y make this so? Prove your observation is true by manipulating your expression in part (a). Solution

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Let X and Y be two continuous random variables with probability dens.pdf

  • 1. Let X and Y be two continuous random variables with probability density functions fX (x) and fY (y). (a) Determine an expression for the density of their difference, fXY , if X and Y are independent. (b) Use your expression to compute the density for X Y for X Unif[0, 1] and Y Unif[0,1]. (c) What is the density of the sum X+Y for XUnif [0,1] and Y Unif [0,1]? (d) How are the answers to parts (b) and (c) similar? What assumptions on X and Y make this so? Prove your observation is true by manipulating your expression in part (a). Solution