Question: Problem LetXandYbe two independentN(0,1)random variables, andU=X+Y Find the conditional PDF ofUgivenX=x,fU|X(u|x). Find the PDF ofU , fU(u). Find the conditional PDF ofX,givenU=u, fX|U(x|u). FindE[X|U=u] andVar(X|U=u)

Problem

LetXandYbe two independentN(0,1)random variables, andU=X+Y

  1. Find the conditional PDF ofUgivenX=x,fU|X(u|x).
  2. Find the PDF ofU , fU(u).
  3. Find the conditional PDF ofX,givenU=u, fX|U(x|u).
  4. FindE[X|U=u] andVar(X|U=u)

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