d$.$ For a system with flip$-$flop $t{s}_s=t_h=100ps,$ a clock frequency of $1$ GHz $,$ and the transition frequency of $10$ MHz $,$ what is the probability of the system entering metastable state?

e$.$ From the system mentioned in part $($d$),$ given that $T_s=tcQ=100ps,$ with the same transition frequency given in part $($d$),$ calculate the probability of failure.

f$.$ From the probability of failure calculated in part $($e$),$ calculate the frequency of failure of the system mentioned in part $($d$).$

g$.$ From the frequency of failure calculated in part $($f$),$ calculate the mean time to failure $($MTTF$)$ of the system. Does the system has an acceptable MTTF$?$ What is the possible cause of this issue?