Homework SourseLet X Y and Z be three independent N11 random variables Find
Let X, Y, and Z be three independent N(1,1) random variables. Find E[XY|Y+Z=1].
Solution
E[XY|Y+Z=1]=E[X]E[Y|Y+Z=1] = E[Y|Y+Z=1]
NOTE: E[Y|Y+Z=1]=E[Z|Y+Z=1] (By symmetry)
E[Y|Y+Z=1]+E[Z|Y+Z=1]=E[Y+Z|Y+Z=1]=1
THEREFORE:
E[Y|Y+Z=1]=1/2
E[XY|Y+Z=1]=1/2
![Let X, Y, and Z be three independent N(1,1) random variables. Find E[XY|Y+Z=1].SolutionE[XY|Y+Z=1]=E[X]E[Y|Y+Z=1] = E[Y|Y+Z=1] NOTE: E[Y|Y+Z=1]=E[Z|Y+Z=1] (By s](/WebImages/3/let-x-y-and-z-be-three-independent-n11-random-variables-find-971805-1761499659-0.webp "Let X, Y, and Z be three independent N(1,1) random variables. Find E[XY|Y+Z=1].SolutionE[XY|Y+Z=1]=E[X]E[Y|Y+Z=1] = E[Y|Y+Z=1] NOTE: E[Y|Y+Z=1]=E[Z|Y+Z=1] (By s")
