As the final rider in the final 60 km time trial of the Tour de France, Roy must finish in time T<1 hour to win the Tour. He has the choice of bike made of (1) car- bon fiber or (2) titanium. On the carbon fiber bike, his speed V over the course is the continuous uniform random variable with E[V] 58 km/hr and Var [V]- 12. On the titanium bike, V is the exponential random variable with E[V]- 60 km/hr
(a) Roy chooses his bike to maximize P[W], the probability he wins the Tour. Which bike does Roy choose and what P[W]