solve question c

1. Let (Sn)n0 be symmetric simple random walk on Z, started at S0=0. Let Rn= min{S0,S1,,Sn} be the running minimum of the walk over the first n steps. Use the reflection principle to complete the following exercises. (c) Prove that for any r0, we have P(Rnr)=2P(Snr)P(Sn=r). Note: Since P(Snr)=2P(Snr) for all r