2.14 Let X1; X2; ... be independent and identically distributed Bernoulli random variables with values 6 1 that have equal probability of 1=2. Let K1 and K2 be positive integers, and define N as follows: N 5 minfnjSn 5 K1 or Sn 5 2K2g where Sn 5 Xn k51 Xk n 5 1; 2; ... is called a symmetric random walk.

a. Show that E½N ,N.

b. Show that P S½  n 5 K1 5 K2 K1 1 K2 .