Assume an asset price S_t follows the geometric Brownian motion, dS_t= S_td_t+ S_tdW_t, where and are constants and r is the risk-free rate.

1. Using the Itos Lemma find the stochastic differential equation satisfied by the process X_t= S_tⁿ, where n is a constant.

2. Compute E[X_t] and Var[X_t].

3. Using the Itos Lemma find the stochastic differential equation satisfied by the process Y_t= S_te^rt.