1. Find how much a stock would move given a risk-free rate of 1.99 over a period of 0.47 part of a year (this is the value of 'a' or the risk-free movement in binomial pricing). 

2. Find the probability of an up movement in a binomial model (proby(u)=(a-d)/(u-d). Given that the time period between nodes is 0.56 part of a year, the stock has a standard deviation of 24.5%, and the risk-free rate is 0.65%. 

3. Find the probability of a down movement in a binomial model give the probability of an up movement is 67.22%.