Suppose that current stock price is $20 and pays no dividends. Its annualized volatility is 15% and stock return 2.5% (i.e. we assume that the stock price follows.

1) Write the probability density function for the stock in 1 month, 6 months, 1 year, and 2 years.

2) Write the same probability density functions in risk-neutral world assuming constant interest rate 1.5% per year and stock pays no dividends.