=+6. Read Example 4.2.4 on Fibonacci numbers. Consider a probability model whose sample space is the collection of tilings of a checkerboard 5.8 Problems 119 row by square pieces and dominoes. If we assign equal probability to each of the fn possible tilings of a row of length n, then the most pertinent random variable is the number of dominoes Dn in a random tiling. Prove that E(Dn) = 1 fn n

−1 i=1 fi−1fn−i−1

= 1 fn



j fjfn−2−j using the conventions f0 = 1 and fi = 0 for i < 0 and the representation Dn =

n

−1 i=1 Ci,