A rating system features two non$-$default rating classes A and B and a defiult class D$.$ Assume that we observe the history of $30$ firms over one year, of which $10$ start in class A and $20$ in class B$,$ After $4$ months one A$-$rated company is downgraded to B and stays there for the rest of the ycar. Over the same period one B$-$rated company is upgraded after $3$ months and remains in class A until the end of the period. Finally, a B$-$rated company defaults after $9$ months and does not recover. $-$ Calculate the transition matrix according to the cohort method. b$.$ Calculate the second row of the generator matrix for the above example according to the continuous $($Lando$/$Skodeberg$)$ method.