Consider the following two stocks:

$t=0$

$t=1$

$t=2$

The first number in each pair above is the value of stock $x$ at that node, while the second

number is the value of stock Y$.$ Each time period represents one year.

$($a$)$ Calculate all state prices, and risk neutral probabilities.

$($b$)$ What is the risk$-$free spot $(1-$year$)$ rate in state U$?$ In state D$?$ And at $t=0?$

$($c$)$ What is the annualized return on a two$-$year zero coupon bond at $t=0?$

$($d$)$ How does this compare with the annualized expected return on rolling over one$-$year

zero coupon bonds for the next two years? What does this mean with regards to the

expectations hypothesis? I know how to calculate question a$,$ but do not understand question b c d$.$ Please give details step, especially how to calculate risk$-$free rate from state pricing tree model.