A coin had tossed three times. Let ##X##- number of tails and ##Y##- number of heads. Find the expected value and variance ##Z=XY##.
My solution:
We know, that ##Y=3-X##, so ##Z=(3-X)X## for ##X=0,1,2,3##.
##Z=2## for ##X=1,2## and ##Z=0## for ##X=3,0##
So, ##E(Z)=E((3-X)X))= 2 \cdot ⅜ +2 \cdot...